(Originally posted on Sunday, 2 October 2016)
Wow! What a cool tribute-video! My favourite actor in two of my favourite movies: The Terminator and Aliens! He was awesome in these awesome movies!
Everybody remembers these movies for the roles of Arnold Schwarzenegger and Sigourney Weaver (respectively), but the next main actor in BOTH of these movies was Michael Biehn! He was perfect in the roles of Kyle Reese and Dwayne Hicks!
PS. I prefer Aliens over The Terminator, but chronologically The Terminator was first.
Tuesday, 31 March 2015
A constant grin of true happiness (thanks to Ghostbusters: Afterlife)
(Originally posted on Sunday, 21 November 2021)
We (me and my children) have just come back from the cinema and I have to say this: throughtout the movie Ghostbusters: Afterlife I had a constant grin of true happiness! Well, many times I was smiling broadly or laughing out loud! Great job, guys!
We (me and my children) have just come back from the cinema and I have to say this: throughtout the movie Ghostbusters: Afterlife I had a constant grin of true happiness! Well, many times I was smiling broadly or laughing out loud! Great job, guys!
I'm all out of bubblegum
(Originally posted on Friday, 1 January 2021)
From the movie They Live (1988).
Monday, 30 March 2015
Sunday, 29 March 2015
I saw a guy in a coffee-house today
I saw a guy in a coffee-house today. Without a phone. Without a laptop. He sat, stared through a window and drank coffee. Like a psychopath.
(Tuesday, 29 December 2015)
(Tuesday, 29 December 2015)
Dear Santa Claus
(Originally posted on Sunday, 6 December 2020)
“Dear Santa Claus.
This year I would like to have slim figure and huge money.
PS. Please, make no mistake, like you did last year.”
“Dear Santa Claus.
This year I would like to have slim figure and huge money.
PS. Please, make no mistake, like you did last year.”
Saturday, 28 March 2015
A fair scoring system in racing competitions
(Originally posted on Monday, 17 May 2021)
While playing various computer racing games I had been using my own scoring system (in a spreadsheet, just for fun) that awarded points for the top-10 places. Old scoring systems, both in computer games and in real life competitions, awarded points for only top-6 places. I thought that my scoring system was “fair”, but I have just realised that it wasn't quite like that.
Thanks to my in-depth analysis of the current FIA scoring system (points: 25, 18, 15, 12, 10, 8, 6, 4, 2, 1) I have finally realised what a fair scoring system should be like. By the way, the current FIA scoring system is NOT fair/consistent!
In the end I have created a new, near-perfect scoring system that is very easy to remember and use! Points: 30, 22, 16, 12, 9, 7, 5, 4, 3, 2, 1.
What is a “fair scoring system” in racing competitions? It’s a scoring system where the same “rules” apply to ALL the places that are awarded points. Which means …?
Let’s analyse two examples from a fictional season with 10 races, but with the current FIA scoring system (points: 25, 18, 15, 12, 10, 8, 6, 4, 2, 1).
Example I.
Ia. Driver A (8 wins and 2 non-finishes) vs. driver B (10 second places).
Obviously the driver A should win the title because the 2 non-finishes could have been caused by his opponents and/or by a mechanical failure of his car and the driver B was not able to win even a single race! This rule is true in the FIA scoring system:
Driver A: 8 * 25 points = 200 points
Driver B: 10 * 18 points = 180 points
Ib. Driver A (8 second places and 2 non-finishes) vs. driver B (10 third places) + all the races won by 1 driver (the winner of the title).
The rule is exactly the same: the driver A should finish second because the 2 non-finishes could have been caused by his opponents and/or by a mechanical failure of his car and the driver B was not able to finish second even in a single race! This rule is NOT true in the FIA scoring system:
Driver A: 8 * 18 points = 144 points
Driver B: 10 * 15 points = 150 points
So, the FIA scoring system is inconsistent on different “steps of the ladder” and this is why it’s not fair.
Example II.
IIa. Driver A (6 wins and 4 non-finishes) vs. driver B (10 third places) + all the remaining wins and all the second places evenly split between several different drivers (overall they are all behind the drivers A and B).
Obviously the driver A should win the title because the driver B was not able to finish SECOND even in a single race! This rule is true in the FIA scoring system, but only thanks to a tiebreaker:
Driver A: 6 * 25 points = 150 points
Driver B: 10 * 15 points = 150 points
The number of wins would be the tiebreaker.
IIb. Driver A (6 second places and 4 non-finishes) vs. driver B (10 fourth places) + all the remaining second places and all the third places evenly split between several different drivers (overall they are all behind the drivers A and B) + all the races won by 1 driver (the winner of the title).
The rule is exactly the same: the driver A should finish second because the driver B was not able to finish THIRD even in a single race! This rule is NOT true in the FIA scoring system:
Driver A: 6 * 18 points = 108 points
Driver B: 10 * 12 points = 120 points
So, the FIA scoring system is inconsistent on different “steps of the ladder” and this is why it’s not fair.
Please notice that even if you don't agree with the rules above and you apply a different rule then the rule (any rule) should be true for all the “steps of the ladder”. I gave the 2 rules above as EXAMPLES, just to show you that the FIA scoring system is inconsistent on different “steps of the ladder”, which proves that it’s not fair.
How to create a fair scoring system in racing?
Obviously the starting point should be the difference between the first and the second place (depending on various factors), but all the following places have to roughly maintain the ratio between the first and the second place. Obviously the difference between the first place and the third place should also be roughly maintained (by default) for all the following pairs of drivers being two places apart (2 and 4, 3 and 5, 4 and 6, …). It should give you a near-perfect scoring system – the points are total values, so there will always be some slight “fluctuations”, especially at the lower places. Please notice that such a fair scoring system should be consistent on every “step of the ladder”, no matter what rule (of comparing drivers) you invent/analyse.
My near-perfect scoring system that is very easy to remember:
points: 30, 22, 16, 12, 9, 7, 5, 4, 3, 2, 1
Differences between places: 8, 6, 4, 3, 2, 2, 1, 1, 1, 1
Number of places that are awarded points: 11
The sum of points for all the places: 111
Points in reference to the previous place: 1.364, 1.375, 1.333, 1.333, 1.286, 1.400, 1.250, 1.333, 1.500, 2.000.
Points in reference to the place two places behind: 1.875, 1.833, 1.778, 1.714, 1.800, 1.750, 1.667, 2.000, 3.000
Verification:
Ia. Driver A (8 wins and 2 non-finishes) vs. driver B (10 second places).
Driver A: 8 * 30 points = 240 points
Driver B: 10 * 22 points = 220 points
Ib. Driver A (8 second places and 2 non-finishes) vs. driver B (10 third places) + all the races won by 1 driver (the winner of the title).
Driver A: 8 * 22 points = 176 points
Driver B: 10 * 16 points = 160 points
IIa. Driver A (6 wins and 4 non-finishes) vs. driver B (10 third places) + all the remaining wins and all the second places evenly split between several different drivers (overall they are all behind the drivers A and B).
Driver A: 6 * 30 points = 180 points
Driver B: 10 * 16 points = 160 points
IIb. Driver A (6 second places and 4 non-finishes) vs. driver B (10 fourth places) + all the remaining second places and all the third places evenly split between several different drivers (overall they are all behind the drivers A and B) + all the races won by 1 driver (the winner of the title).
Driver A: 6 * 22 points = 132 points
Driver B: 10 * 12 points = 120 points
Practically flawless scoring system that is very easy to remember! Boy, I am proud of myself!
PS. You can create many different fair scoring systems in racing competitions, each with a particular ratio between places and a particular number of places that are awarded points. The problem is that the number of points for the first place rises very quickly, so with every additional place that is awarded points, the system is harder to remember and use. This is why I am so proud of myself – the scoring system that I have created is very easy to remember and use!
While playing various computer racing games I had been using my own scoring system (in a spreadsheet, just for fun) that awarded points for the top-10 places. Old scoring systems, both in computer games and in real life competitions, awarded points for only top-6 places. I thought that my scoring system was “fair”, but I have just realised that it wasn't quite like that.
Thanks to my in-depth analysis of the current FIA scoring system (points: 25, 18, 15, 12, 10, 8, 6, 4, 2, 1) I have finally realised what a fair scoring system should be like. By the way, the current FIA scoring system is NOT fair/consistent!
In the end I have created a new, near-perfect scoring system that is very easy to remember and use! Points: 30, 22, 16, 12, 9, 7, 5, 4, 3, 2, 1.
What is a “fair scoring system” in racing competitions? It’s a scoring system where the same “rules” apply to ALL the places that are awarded points. Which means …?
Let’s analyse two examples from a fictional season with 10 races, but with the current FIA scoring system (points: 25, 18, 15, 12, 10, 8, 6, 4, 2, 1).
Example I.
Ia. Driver A (8 wins and 2 non-finishes) vs. driver B (10 second places).
Obviously the driver A should win the title because the 2 non-finishes could have been caused by his opponents and/or by a mechanical failure of his car and the driver B was not able to win even a single race! This rule is true in the FIA scoring system:
Driver A: 8 * 25 points = 200 points
Driver B: 10 * 18 points = 180 points
Ib. Driver A (8 second places and 2 non-finishes) vs. driver B (10 third places) + all the races won by 1 driver (the winner of the title).
The rule is exactly the same: the driver A should finish second because the 2 non-finishes could have been caused by his opponents and/or by a mechanical failure of his car and the driver B was not able to finish second even in a single race! This rule is NOT true in the FIA scoring system:
Driver A: 8 * 18 points = 144 points
Driver B: 10 * 15 points = 150 points
So, the FIA scoring system is inconsistent on different “steps of the ladder” and this is why it’s not fair.
Example II.
IIa. Driver A (6 wins and 4 non-finishes) vs. driver B (10 third places) + all the remaining wins and all the second places evenly split between several different drivers (overall they are all behind the drivers A and B).
Obviously the driver A should win the title because the driver B was not able to finish SECOND even in a single race! This rule is true in the FIA scoring system, but only thanks to a tiebreaker:
Driver A: 6 * 25 points = 150 points
Driver B: 10 * 15 points = 150 points
The number of wins would be the tiebreaker.
IIb. Driver A (6 second places and 4 non-finishes) vs. driver B (10 fourth places) + all the remaining second places and all the third places evenly split between several different drivers (overall they are all behind the drivers A and B) + all the races won by 1 driver (the winner of the title).
The rule is exactly the same: the driver A should finish second because the driver B was not able to finish THIRD even in a single race! This rule is NOT true in the FIA scoring system:
Driver A: 6 * 18 points = 108 points
Driver B: 10 * 12 points = 120 points
So, the FIA scoring system is inconsistent on different “steps of the ladder” and this is why it’s not fair.
Please notice that even if you don't agree with the rules above and you apply a different rule then the rule (any rule) should be true for all the “steps of the ladder”. I gave the 2 rules above as EXAMPLES, just to show you that the FIA scoring system is inconsistent on different “steps of the ladder”, which proves that it’s not fair.
How to create a fair scoring system in racing?
Obviously the starting point should be the difference between the first and the second place (depending on various factors), but all the following places have to roughly maintain the ratio between the first and the second place. Obviously the difference between the first place and the third place should also be roughly maintained (by default) for all the following pairs of drivers being two places apart (2 and 4, 3 and 5, 4 and 6, …). It should give you a near-perfect scoring system – the points are total values, so there will always be some slight “fluctuations”, especially at the lower places. Please notice that such a fair scoring system should be consistent on every “step of the ladder”, no matter what rule (of comparing drivers) you invent/analyse.
My near-perfect scoring system that is very easy to remember:
points: 30, 22, 16, 12, 9, 7, 5, 4, 3, 2, 1
Differences between places: 8, 6, 4, 3, 2, 2, 1, 1, 1, 1
Number of places that are awarded points: 11
The sum of points for all the places: 111
Points in reference to the previous place: 1.364, 1.375, 1.333, 1.333, 1.286, 1.400, 1.250, 1.333, 1.500, 2.000.
Points in reference to the place two places behind: 1.875, 1.833, 1.778, 1.714, 1.800, 1.750, 1.667, 2.000, 3.000
Verification:
Ia. Driver A (8 wins and 2 non-finishes) vs. driver B (10 second places).
Driver A: 8 * 30 points = 240 points
Driver B: 10 * 22 points = 220 points
Ib. Driver A (8 second places and 2 non-finishes) vs. driver B (10 third places) + all the races won by 1 driver (the winner of the title).
Driver A: 8 * 22 points = 176 points
Driver B: 10 * 16 points = 160 points
IIa. Driver A (6 wins and 4 non-finishes) vs. driver B (10 third places) + all the remaining wins and all the second places evenly split between several different drivers (overall they are all behind the drivers A and B).
Driver A: 6 * 30 points = 180 points
Driver B: 10 * 16 points = 160 points
IIb. Driver A (6 second places and 4 non-finishes) vs. driver B (10 fourth places) + all the remaining second places and all the third places evenly split between several different drivers (overall they are all behind the drivers A and B) + all the races won by 1 driver (the winner of the title).
Driver A: 6 * 22 points = 132 points
Driver B: 10 * 12 points = 120 points
Practically flawless scoring system that is very easy to remember! Boy, I am proud of myself!
PS. You can create many different fair scoring systems in racing competitions, each with a particular ratio between places and a particular number of places that are awarded points. The problem is that the number of points for the first place rises very quickly, so with every additional place that is awarded points, the system is harder to remember and use. This is why I am so proud of myself – the scoring system that I have created is very easy to remember and use!
The easiest way to tie a tie
(Originally posted on Monday, 15 August 2016)
My way of tying a tie is a rare one, but also the easiest one. My father taught me how to do it and he must had learned it during his college times, because his father (my grandfather) used to tie a tie in a different way.
The CRUCIAL thing is to start with a tie lying on your neck on the left-side!!!
I made some pictures from the point of view of a person tying a tie – I don't understand people picturing it from a different perspective.
My way of tying a tie is a rare one, but also the easiest one. My father taught me how to do it and he must had learned it during his college times, because his father (my grandfather) used to tie a tie in a different way.
The CRUCIAL thing is to start with a tie lying on your neck on the left-side!!!
I made some pictures from the point of view of a person tying a tie – I don't understand people picturing it from a different perspective.
Friday, 27 March 2015
The earliest sunset occurs earlier than the shortest day
The earliest sunset occurs earlier than the shortest day – this is a kind of trivia I “discovered” a few years ago and I was VERY surprised. The site below shows sunrise and sunset times and you can check it yourself.
For Washington, DC, USA the times are:
Sunrise time on December 7 is 7:13:45 am.
Sunset time on December 7 is 4:45:58 pm (the earliest sunset).
Day length on December 7 is 09:32:13.
Sunrise time on December 21 is 7:23:21 am.
Sunset time on December 21 is 4:49:41 pm.
Day length on December 21 is 09:26:20 (the shortest day).
Sunrise time on January 4 is 7:26:58 am (the latest sunrise).
Sunset time on January 4 is 4:59:35 pm.
Day length on January 4 is 09:32:37.
http://sunrise-sunset.org/search?location=washington+dc
Here are screenshots from December 2015 and January 2016:
(Saturday, 5 December 2015)
For Washington, DC, USA the times are:
Sunrise time on December 7 is 7:13:45 am.
Sunset time on December 7 is 4:45:58 pm (the earliest sunset).
Day length on December 7 is 09:32:13.
Sunrise time on December 21 is 7:23:21 am.
Sunset time on December 21 is 4:49:41 pm.
Day length on December 21 is 09:26:20 (the shortest day).
Sunrise time on January 4 is 7:26:58 am (the latest sunrise).
Sunset time on January 4 is 4:59:35 pm.
Day length on January 4 is 09:32:37.
http://sunrise-sunset.org/search?location=washington+dc
Here are screenshots from December 2015 and January 2016:
(Saturday, 5 December 2015)
The earliest sunset occurs earlier than the shortest day, but the latest sunset occurs later than the longest day
(Originally posted on Sunday, 13 June 2021)
Several years ago I described my “discovery” that the earliest sunset occurs earlier than the shortest day:
The earliest sunset occurs earlier than the shortest day
I thought that a similar rule was true for the longest day, but it's not true! Everything is reversed during the summer!
This time I prepared a double example (for longest and shortest days), but I used a different city (Edmonton in Canada), so the dates are not so spread out.
1. The longest day and the latest sunset.
https://sunrise-sunset.org/search?location=edmonton&year=2021&month=6
In Edmonton the longest day is 20 June 2021, but the latest sunset is on 24 June 2021.
2. The shortest day and the earliest sunset.
https://sunrise-sunset.org/search?location=edmonton&year=2021&month=12
In Edmonton the shortest day is 20 December 2021, but the earliest sunset is on 12 December 2021.
Several years ago I described my “discovery” that the earliest sunset occurs earlier than the shortest day:
The earliest sunset occurs earlier than the shortest day
I thought that a similar rule was true for the longest day, but it's not true! Everything is reversed during the summer!
This time I prepared a double example (for longest and shortest days), but I used a different city (Edmonton in Canada), so the dates are not so spread out.
1. The longest day and the latest sunset.
https://sunrise-sunset.org/search?location=edmonton&year=2021&month=6
In Edmonton the longest day is 20 June 2021, but the latest sunset is on 24 June 2021.
2. The shortest day and the earliest sunset.
https://sunrise-sunset.org/search?location=edmonton&year=2021&month=12
In Edmonton the shortest day is 20 December 2021, but the earliest sunset is on 12 December 2021.
Thursday, 26 March 2015
Aliens director’s cut trivia
The
theatrical version of Aliens was great on its own, but the director’s cut of
Aliens is waaay better. I was blown away when I saw what great scenes were
removed in the original release, just to make the film shorter. They removed 17
(SEVENTEEN) minutes of the film!!! And all of the removed scenes were perfectly
fitting to the story. Some of them are actually very important, like a scene
when Ellen Ripley finds out that her daughter is dead or a scene showing how (and
why) colonists found alien eggs. Those scenes make the introduction part of the
film longer, but better considering the rising tension. Some of the other removed
scenes are very fun, like Hudson’s speech or several scenes with automatic sentry
guns.
All the
actors were great in this film, especially Sigourney Weaver as Ellen Ripley, Michael
Biehn as Corporal Dwayne Hicks, Bill Paxton as Private William Hudson and Lance
Henriksen as Bishop. Newt (the little girl) was played by Carrie Henn. James
Cameron chose her, because she had no casting experience and she didn’t smile
after saying her line, unlike other girls who were auditioned for the role.
Aliens is the only film she has played in.
Do you know
that, before the filming started, actors who played Marines together went
through a military training (for two weeks), so they could play a
believable well-working unit? Do you know that a picture of Ellen Ripley’s
daughter (seen in the director’s cut) is actually a picture of Sigourney Weaver’s
mother? Do you know that Newt’s brother (seen in the director’s cut) is
actually Carrie Henn’s real brother? Do you know that one of the dropships was
named “Smart Ass” and it had a slogan: “We aim by PFM” – a shortcut form
“Pure Fucking Magic”?
There are
tons of fun trivia about Aliens, especially about its production. This film was
made in 1985-1986 in the era before digital special effects. Almost everything
seen in Aliens was filmed in a real world environment and it still looks great
today. James Cameron is praised for Titanic and Avatar, but to me his biggest
achievement as a director (and as a screenwriter as well) is the film Aliens.
There is a
great site about Aliens http://film.org.pl/fx/aliensmenu.html
where you can find almost everything about Aliens with EXAMPLES, like pictures
showing scenes which were removed in the theatrical version or pictures showing
scenes where a particular special effect was used. However, there are two
problems – this site is not in English and some of its sub-sites are show with
errors and without pictures. Fortunately a Google translation can fix those problems
and everything can be seen properly. The translation itself is not perfect, but
it is understandable in most cases. Of course you can learn all about Aliens
somewhere else, but without all those pictures.
Below are
links to Google translations of this site and all its sub-sites. They display
fine on my computer. Otherwise try pressing “stop loading” at the right moment.
Please notice
that in Polish the word “obcy” is both a singular form (“alien”) and a plural
form (“aliens”). To distinguish the first and the second film in the series in Poland the film Aliens was titled “Alien(s) – The Decisive Battle” (“Obcy – Decydujące
Starcie”). It turned out later that it was not decisive at all. :) Apparently the Google translator “knows”
about the Polish title because after translation it sometimes appear as “Aliens – Aliens”, which makes no
sense otherwise.
Production
http://translate.google.pl/translate?sl=pl&tl=en&js=n&prev=_t&hl=pl&ie=UTF-8&u=http%3A%2F%2Ffilm.org.pl%2Ffx%2Faliensr.html
Special
effects
http://translate.google.pl/translate?sl=pl&tl=en&js=n&prev=_t&hl=pl&ie=UTF-8&u=http%3A%2F%2Ffilm.org.pl%2Ffx%2Faliense.html
Director’s
cut
http://translate.google.pl/translate?sl=pl&tl=en&js=n&prev=_t&hl=pl&ie=UTF-8&u=http%3A%2F%2Ffilm.org.pl%2Fdir_cut%2Faliens.html
Introduction
and menu (logically this should be the first link)
http://translate.google.pl/translate?sl=pl&tl=en&js=n&prev=_t&hl=pl&ie=UTF-8&u=http%3A%2F%2Ffilm.org.pl%2Ffx%2Faliensmenu.html
Removed
scenes (scenes which didn’t make it even to the director’s cut)
http://translate.google.pl/translate?sl=pl&tl=en&js=n&prev=_t&hl=pl&ie=UTF-8&u=http%3A%2F%2Ffilm.org.pl%2Ffx%2Falienss.html
Evolution
of screenplay (without any pictures)
http://translate.google.pl/translate?sl=pl&tl=en&js=n&prev=_t&hl=pl&ie=UTF-8&u=http%3A%2F%2Ffilm.org.pl%2Ffx%2Faliensscr.html
Payroll
http://translate.google.pl/translate?sl=pl&tl=en&js=n&prev=_t&hl=pl&ie=UTF-8&u=http%3A%2F%2Ffilm.org.pl%2Ffx%2Faliensl.html
Here’s another site from the same main site. There’s a unique picture at the end.
(Monday, 22 July 2013)
Wednesday, 25 March 2015
The Big Bang Theory
The Big Bang Theory is a great sitcom series featuring a character, named Sheldon Cooper, who has Asperger Syndrome. It’s hilarious to see how he analyses everything logically, with hardly any social skills. The below fragment is also a great example of how important his habits/routines are to him.
(Saturday, 13 July 2013)
(Saturday, 13 July 2013)
Tuesday, 24 March 2015
My Family – my favourite sitcom ever
My Family is my favourite sitcom ever. It’s done in a very intelligent way that suits my taste perfectly.
I rarely boast about something, but here I come: I have never spent so much money for my own entertainment before – I have bought a box with 22 My Family DVDs – complete series 1-11 plus 9 Christmas specials!
The synopsis from the cover of the first DVD is quite good:
“Ben, a dentist, and Susan, the worst cook in the world, are certainly loving, caring parents, they just have a problem showing it. Ben seems to be confused as to how much time and money his kids demand from him. Susan has to juggle motherhood, a career and a husband and does not have enough time to manage everything including improving her cooking skills. Nick is always working on his next hair-brained scheme to keep him amused. Janey, like any normal teenage daughter feels that her parents are seriously embarrassing whilst Michael keeps his head in his books to get away from the noise.”
The box has one HUGE advantage – it features English subtitles! They are labelled “English for the Hard of Hearing”, but they are perfect for a person like me – English is not my native language and I have trouble understand everything by ear. While watching the DVDs I can always read the subtitles and understand everything anyway. Perfect! From what I hear by ear I must say that the subtitles are done very well – there is hardly anything omitted.
This great sitcom is rather new (was broadcasted by BBC between 2000 and 2011), but there are no good examples of it on YouTube. The ones that are on YouTube are very short and seem strange because they are taken out of context. Moreover there are NO examples with English subtitles. This is why I have created an example by myself. I did it using my mobile phone, so the quality is bad, but at least you can see how lively My Family episodes are. Enjoy!
(Sunday, 13 July 2014)
PS. My film was blocked. I can't believe it! There are no samples of this great sitcom with subtitles, so I was doing the copyright owners a favour and they blocked it! Ridiculous.
PS2. I found the episode on the net, but it is without subtitles. Shame.
I rarely boast about something, but here I come: I have never spent so much money for my own entertainment before – I have bought a box with 22 My Family DVDs – complete series 1-11 plus 9 Christmas specials!
The synopsis from the cover of the first DVD is quite good:
“Ben, a dentist, and Susan, the worst cook in the world, are certainly loving, caring parents, they just have a problem showing it. Ben seems to be confused as to how much time and money his kids demand from him. Susan has to juggle motherhood, a career and a husband and does not have enough time to manage everything including improving her cooking skills. Nick is always working on his next hair-brained scheme to keep him amused. Janey, like any normal teenage daughter feels that her parents are seriously embarrassing whilst Michael keeps his head in his books to get away from the noise.”
The box has one HUGE advantage – it features English subtitles! They are labelled “English for the Hard of Hearing”, but they are perfect for a person like me – English is not my native language and I have trouble understand everything by ear. While watching the DVDs I can always read the subtitles and understand everything anyway. Perfect! From what I hear by ear I must say that the subtitles are done very well – there is hardly anything omitted.
This great sitcom is rather new (was broadcasted by BBC between 2000 and 2011), but there are no good examples of it on YouTube. The ones that are on YouTube are very short and seem strange because they are taken out of context. Moreover there are NO examples with English subtitles. This is why I have created an example by myself. I did it using my mobile phone, so the quality is bad, but at least you can see how lively My Family episodes are. Enjoy!
(Sunday, 13 July 2014)
PS. My film was blocked. I can't believe it! There are no samples of this great sitcom with subtitles, so I was doing the copyright owners a favour and they blocked it! Ridiculous.
PS2. I found the episode on the net, but it is without subtitles. Shame.
Monday, 23 March 2015
Aliens' 30th anniversary
(Originally posted on Wednesday, 14 September 2016)
I wrote about this awesome movie here:
Aliens director’s cut trivia
This year the movie Aliens was celebrating its 30th anniversary. There are some cool articles about it:
http://screenrant.com/aliens-30-year-anniversary/
http://www.denofgeek.com/us/movies/aliens/257290/aliens-30th-anniversary-15-things-we-learned
http://www.latimes.com/entertainment/herocomplex/la-et-hc-comic-con-aliens-30th-panel-20160723-snap-story.html
http://www.usatoday.com/story/life/movies/2016/07/17/where-stars-aliens-30-years-later/86817532/
http://www.forbes.com/sites/simonthompson/2016/08/01/michael-biehn-talks-aliens-30th-anniversary-his-production-company-and-his-alien-future/#4412fb094106
There were many great actors in Aliens, but my favourite one has always been Michael Biehn. He was fantastic in Aliens! And in Terminator too! Here is a HUGE article about this actor:
https://lebeauleblog.com/2014/03/08/what-the-hell-happened-to-michael-biehn/
Some time ago I learned that he had had an alcohol problem (much later in his career than Aliens) and I was very surprised. Well, anybody can get addicted to something, but Michael Biehn? One of my favourite actors ever? Yeah, alcohol is easy to obtain and perfectly legal, so why not? I myself drink hardly any alcohol, but some of my colleagues at work are SURE that one beer a day is not a problem.
Anyway, I found a very funny anecdote about Biehn, but I doubt if it is true. It's more like a joke. I found it here:
http://www.avpgalaxy.net/forum/index.php?topic=25598.15
Quote from the user “maledoro”:
I have a Michael Biehn story to share with you all. A few years back, my (then) girlfriend and I were walking through NYC and saw this unshaven, but well-dressed guy standing on a corner with a 40 in his hand yelling, "I was Hicks! I was Hicks!"
My girlfriend said, "He looks like a hick...", and told her, "Wait just a sec. I think I know this guy." We walked closer, and I asked, "Sir? Are you Michael Biehn?" The guy's crazed look softened a bit and he said, "Yes, I am!"
My girlfriend asked, "You? A terrible drunk like you is Michael Biehn?" The guy looked at her and said, "Whattya mean 'terrible'? I'm one of the best drunks in this city!"
I wrote about this awesome movie here:
Aliens director’s cut trivia
This year the movie Aliens was celebrating its 30th anniversary. There are some cool articles about it:
http://screenrant.com/aliens-30-year-anniversary/
http://www.denofgeek.com/us/movies/aliens/257290/aliens-30th-anniversary-15-things-we-learned
http://www.latimes.com/entertainment/herocomplex/la-et-hc-comic-con-aliens-30th-panel-20160723-snap-story.html
http://www.usatoday.com/story/life/movies/2016/07/17/where-stars-aliens-30-years-later/86817532/
http://www.forbes.com/sites/simonthompson/2016/08/01/michael-biehn-talks-aliens-30th-anniversary-his-production-company-and-his-alien-future/#4412fb094106
There were many great actors in Aliens, but my favourite one has always been Michael Biehn. He was fantastic in Aliens! And in Terminator too! Here is a HUGE article about this actor:
https://lebeauleblog.com/2014/03/08/what-the-hell-happened-to-michael-biehn/
Some time ago I learned that he had had an alcohol problem (much later in his career than Aliens) and I was very surprised. Well, anybody can get addicted to something, but Michael Biehn? One of my favourite actors ever? Yeah, alcohol is easy to obtain and perfectly legal, so why not? I myself drink hardly any alcohol, but some of my colleagues at work are SURE that one beer a day is not a problem.
Anyway, I found a very funny anecdote about Biehn, but I doubt if it is true. It's more like a joke. I found it here:
http://www.avpgalaxy.net/forum/index.php?topic=25598.15
Quote from the user “maledoro”:
I have a Michael Biehn story to share with you all. A few years back, my (then) girlfriend and I were walking through NYC and saw this unshaven, but well-dressed guy standing on a corner with a 40 in his hand yelling, "I was Hicks! I was Hicks!"
My girlfriend said, "He looks like a hick...", and told her, "Wait just a sec. I think I know this guy." We walked closer, and I asked, "Sir? Are you Michael Biehn?" The guy's crazed look softened a bit and he said, "Yes, I am!"
My girlfriend asked, "You? A terrible drunk like you is Michael Biehn?" The guy looked at her and said, "Whattya mean 'terrible'? I'm one of the best drunks in this city!"
Sunday, 22 March 2015
Subordinate, in the presence of the superior
(Originally posted on Friday, 16 September 2016)
Subordinate, in the presence of the superior, should have the wretched and dumb look, so that his understanding of a matter didn't embarrass the superior.
(Reputedly it's a quote from an edict issued in 1708 by Peter I the Great.)
Subordinate, in the presence of the superior, should have the wretched and dumb look, so that his understanding of a matter didn't embarrass the superior.
(Reputedly it's a quote from an edict issued in 1708 by Peter I the Great.)
Saturday, 21 March 2015
Ancient sites
Google
Earth has an in-built feature of rendering 3D images of some buildings or
structures, for example Egyptian Sphinx and Pyramids.
I have found such 3D structures at Machu Picchu an ancient site that I always wanted to visit.
What’s really interesting is the fact that I found there TWO separate structures. One is the well-known Machu Picchu, but the other is a structure I have never heard of. In fact this other site is even more amazing than Machu Picchu, because it is built at the very summit of a nearby mountain. Take a look.
This other structure is called Huayna Picchu or Wayna Picchu.
I found a picture of it at the site
http://www.inkas.com/tours/cuzco_machu_picchu/santillan_photos.html
Here it is (click to enlarge):
As a side note: At the same site there are pictures not only from Machu Picchu, but also from other places. There are some pictures from Cuzco showing something that is called “Incan stonework”.
It looks like this (click to enlarge):
There are some theories that claim these structures were built much earlier than Incan civilization. There are similar theories considering the age of Puma Punku, Baalbek ruins, the Sphinx and the Pyramids. If you are interested in our World's biggest archeological mysteries then check this site:
http://www.atlantisquest.com/Archeology.html
(Sunday, 20 May 2012)
Friday, 20 March 2015
Thursday, 19 March 2015
Binoculars and spotting scopes brightness comparison
(Originally posted on Sunday, 26 July 2020; updated most recently on 23 March 2022)
In the most recent update I have made some changes and I also added new content, based on my additional experience. A year ago I bought a telescope and after some time I realised that the formula described in the present post is useful not only for comparing binoculars and/or spotting scopes, but also for comparing telescopes with particulars eyepieces.
I “discovered” a very interesting thing that can be helpful while deciding what kind of observing equipment to buy.
I have had 8x30 binoculars for a very long time, but recently I decided to buy something with better magnification. I had an opportunity to buy a 30x50 spotting scope for a very low price and I did it. When I compared these two observing tools after getting home I got very surprised.
In most cases while using the 30x50 spotting scope I was able to distinguish only marginally more details than with the 8x30 binoculars! Why? Because everything was much DARKER in the spotting scope and things that were not bright enough were hard to see at all, even though they were bigger.
MOST RECENT UPDATE – PART 1:
For some people it's an ever-going debate what is more important magnification (8x vs. 30x) or aperture (30 vs. 50), but the truth is that aperture on its own is meaningless – your equipment can't improve your own eyes. Looking through a telescope without any magnification would be like looking through some kind of tube. The bigger the aperture the bigger the tube. Would that improve anything? Obviously not.
The naked eye “works at your maximum aperture”, but you can't see things like the rings of Saturn with the naked eye. Well, you can't see them even in binoculars, but they are obvious already in a small telescope (magnification 70x is more than enough to see them). It's also consistent with the fact that it's better to use any kind of binoculars (any kind of magnification) instead of looking at stars with the naked eye (without any magnification).
So, to see more details you need magnification, no doubt about it. This fact alone decides that magnification is more important overall, BUT you have to increase aperture to PREVENT the view from getting too dark (bigger magnification => smaller exit pupil and darker view). And this is exactly what was missing in my 30x50 spotting scope – the magnification was good, but the aperture wasn't up to the task.
As far as binoculars are concerned the brightness is VERY important because it makes the view more “fun”. I bought and compared 8x42 and 10x42 monoculars side by side and I have to say that I can see a little more details and a few more stars (in a particular field of view) in the 10x42 monocular, HOWEVER it feels as if these “more details and more stars” can be seen as a result of “work” rather than “fun”:
1) the field of view is clearly narrower in the 10x42 monocular than in the 8x42 monocular,
2) the image is a little more shaky in the 10x42 monocular than in the 8x42 monocular,
3) the image is clearly darker in the 10x42 monocular than in the 8x42 monocular.
For most people a little more details and a few more stars (in a particular field of view) would not be enough to compensate for the less enjoyable image.
END OF MOST RECENT UPDATE – PART 1.
The observed difference in brightness can be calculated from the above numbers (“8x30” and “30x50”). Obviously we have to ASSUME that everything else is equal. The first number 8x (or 30x) represents magnification or “power” – how many times bigger the observed object appears. The second number 30 (or 50) is aperture – the diameter of each of the objective lenses (the lenses furthest from your eye), given in millimetres.
Let's start with the aperture (the second part of the final formula), because it's more natural. The bigger the aperture – the more light “goes into” the observing tool, so everything should be brighter. The amount of light “going into” the observing tool depends on the AREA of the objective lenses. Let's calculate the respective “going-in” areas:
1) …x30 “going-in” area = PI * R^2 = PI * (30/2)^2 = 3.1416 * 225 = 706.86
2) …x50 “going-in” area = PI * R^2 = PI * (50/2)^2 = 3.1416 * 625 = 1963.5
So if everything else were equal then the brightness of the …x30 observing tool would be 0.36 times of the brightness of the …x50 observing tool (706.86 / 1963.5). The value below 1 means that the …x30 observing tool would be DARKER than the …x50 observing tool. In other words the …x50 observing tool would be 2.7778 times brighter than the …x30 observing tool (1 / 0.36 = 1963.5 / 706.86).
The difference in brightness caused by magnification (“power”) is much more difficult to imagine, but one visual example should be enough to understand. Please remember that this example is NOT about focus and NOT about colours, but about the AMOUNT of light REFLECTED from the observed object that reaches the observing tool. In other words: the smaller objects reflect less light that can be magnified by the observing tool. Again, it's all about areas and again the bigger area improves the brightness, but this time the area is the biggest when the number (magnification) is the smallest!
To make my job easier I drew squares instead of circles, but the idea is clear anyway. The side of all pictures is 480 pixels long. The side of the bigger square is 60 pixels long (magnification of 8x…) and the side of the smaller square is 16 pixels long (magnification of 30x…). The area of the bigger square is 3600 square pixels (60x60) and the area of the smaller square is 256 square pixels (16x16).
As you can see on the last picture there are LESS “pixels of light” stretched (magnified) and this is why the bigger magnification is DARKER.
In reality we can't calculate any REAL areas because in real life there are no pixels to count and we don't know how far away the observed object is. All we can do is to calculate “visual” areas of the two magnifications relatively to each other. Obviously they have to be calculated as circles, not squares.
Assuming that the diameter of the whole visible area is X, then the diameter of the bigger circle (magnification of 8x…) is X/8 and the diameter of the smaller circle (magnification of 30x…) is X/30:
1) 8x… “visual” area = PI * R^2 = PI * ((X/8)/2)^2 = 3.1416 * X^2 / 16^2 = X^2 * 0.012271875
2) 30x… “visual” area = PI * R^2 = PI * ((X/30)/2)^2 = 3.1416 * X^2 / 60^2 = X^2 * 0.000872667
So if everything else were equal then the 8x… observing tool would be 14.0625 times brighter than the 30x… observing tool ((X^2 * 0.012271875) / (X^2 * 0.000872667)). This is exactly the same value as in the example above (3600/256 = 14.0625).
Now we have to combine these two results:
1) if everything else were equal then the brightness of the …x30 observing tool would be 0.36 times of the brightness of the …x50 observing tool,
2) if everything else were equal then the 8x… observing tool would be 14.0625 times brighter than the 30x… observing tool.
We have to simply multiply these two values:
0.36 * 14.0625 = 5.0625
The final value is above 1, so the 8x30 observing tool is 5.0625 times brighter than the 30x50 observing tool. This value explains why everything is much DARKER in my spotting scope and things that are not bright enough are hard to see at all, even though they are bigger than in my binoculars.
Let's simplify the overall formula as much as possible (using also the more natural order):
B&SSBC – Binoculars and Spotting Scopes Brightness Comparison
B&SSBC(A1xA2; B1xB2) = (B1/A1)^2 * (A2/B2)^2
For example:
B&SSBC(8x30; 30x50) = (30/8)^2 * (30/50)^2 = 14.0625 * 0.36 = 5.0625
MOST RECENT UPDATE – PART 2:
My formula works also for telescopes because it’s just a different (greatly simplified) way of comparing exit pupil areas. Below there is my formula with a better (general) name and less confusing “letters”.
EBC – equipment brightness comparison
M – magnification
A – aperture
EBC(M1xA1; M2xA2) = (M2/M1)^2 * (A1/A2)^2
Calculations for comparing exit pupil areas (EPA):
area = Pi * R^2
R = exit pupil/2
exit pupil = A/M
EPA = Pi*R^2 = Pi * (exit pupil/2)^2 = Pi * ((A/M)/2)^2 = Pi * (A/M)^2 * (1/2)^2 = Pi * (A/M * A/M) * 1/4 = Pi * A^2/M^2 * 1/4
EPA1/EPA2 = (Pi * A1^2/M1^2 * 1/4) / (Pi * A2^2/M2^2 * 1/4) = (A1^2/M1^2) / (A2^2/M2^2) = (A1^2/M1^2) * (M2^2/A2^2) = M2^2/M1^2 * A1^2/A2^2 = (M2/M1)^2 * (A1/A2)^2
END OF MOST RECENT UPDATE – PART 2.
The second problem with the 30x50 spotting scope is the fact that it's very hard to use by hand (without a tripod) – very distant observed objects are “jumping” all over the view because you can't keep your hands perfectly steady. For this very reason I ordered another pair of binoculars, this time 12x60 binoculars. Let's compare them to my old binoculars and my new spotting scope:
B&SSBC(12x60; 8x30) = (8/12)^2 * (60/30)^2 = 0.444444 * 4 = 1.777778
B&SSBC(12x60; 30x50) = (30/12)^2 * (60/50)^2 = 6.25 * 1.44 = 9.0000
Now, this is what I call an improvement over my old binoculars – in my new binoculars everything should be larger by 50% ((12-8)/8) AND the brightness should be better by 77%! Both these things combined should make a HUGE difference. We'll see (I will update this post as soon as the my new binoculars arrive and I verify it in reality).
Please notice that B&SSBC values can be calculated is steps:
B&SSBC(12x60; 30x50) = B&SSBC(12x60; 8x30) * B&SSBC(8x30; 30x50) = 1.777778 * 5.0625 = 9.0000
When I was searching various Internet forums about binoculars and spotting scopes I found many suggestions that the 10x50 binoculars are optimal, so let's compare them to the 12x60 binoculars I ordered:
B&SSBC(12x60; 10x50) = (10/12)^2 * (60/50)^2 = 0.6944444 * 1.44 = 1.0000
B&SSBC(10x50; 12x60) = (12/10)^2 * (50/60)^2 = 1.44 * 0.6944444 = 1.0000
EXACTLY the same brightness! So, in my opinion, I ordered the better binoculars – with the same brightness I should be able to see everything bigger by 20%. Using the 12x60 binoculars by hand (without a tripod) should be much easier than using my 30x50 spotting scope by hand, so I should have no problem at all to use them by hand.
On the Internet forums there are many comparisons between 10x50 binoculars and 15x70 binoculars, so let's verify them with my formula:
B&SSBC(10x50; 15x70) = (15/10)^2 * (50/70)^2 = 2.25 * 0.5102 = 1.148
B&SSBC(12x60; 15x70) = (15/12)^2 * (60/70)^2 = 1.5625 * 0.73469 = 1.148
So, 10x50 and 12x60 binoculars should be brighter by 14.8% than 15x70 binoculars. Not that big of a difference, but 15x70 binoculars are much bigger, especially when compared to the 10x50 binoculars AND the bigger magnification makes them harder to use by hand (without a tripod). On the other hand everything will be 50% bigger in the 15x70 binoculars when compared to the 10x50 binoculars, so it's a real toss up. HOWEVER in case of the 12x60 binoculars everything will be only 25% bigger in the 15x70 binoculars, so again the 12x60 binoculars seem like a perfect compromise to me.
Are the 10x50 and 12x60 binoculars the best as far as brightness is concerned? No, they are not! From the binoculars that are usually available there are 8x56 and 9x63 binoculars that are almost TWICE (!!!) as bright, BUT there is a catch (see my comments below calculations):
B&SSBC(8x56; 10x50) = (10/8)^2 * (56/50)^2 = 1.5625 * 1,2544 = 1.96
B&SSBC(8x56; 12x60) = (12/8)^2 * (56/60)^2 = 2.25 * 0.8711111 = 1.96
B&SSBC(9x63; 10x50) = (10/9)^2 * (63/50)^2 = 1.2345679 * 1.5876 = 1.96
B&SSBC(9x63; 12x60) = (12/9)^2 * (63/60)^2 = 1.777778 * 1.1025 = 1.96
However, there is a crucial difference: these binoculars have Exit Pupil of 7 (56/8 and 63/9), instead of 5 (50/3 and 60/12), which can be bad if you are looking at stars with artificial sources of light nearby – under such circumstances your pupils will be smaller than 7mm, which would mean that some brightness of the binoculars will be lost to your eye. What's worse your pupils are getting smaller with age, so such binoculars are good ONLY for young people. By the way, during a day even young people have pupils smaller than 7mm, but there is so much light then that it's not really important. For these very reasons the 8x56 and 9x63 binoculars are called hunting binoculars rather than astronomical binoculars.
On the side note – one of the differences between binoculars is the type of prisms. BAK4 prisms are usually better on the edges than BK7 prisms, especially when there is little light, BUT there may be some exceptions connected with some other details of the prisms. I am not a specialist, so I can't explain anything about prisms. You can Google it on the Internet.
At the end I would like to point out one thing: if you would like to build binoculars or a spotting scope with 15x magnification and the same brightness as the 10x50 and 12x60 binoculars then they would have to be 15x75 binoculars:
B&SSBC(10x50; 15x75) = (15/10)^2 * (50/75)^2 = 2.25 * 0.44444 = 1.000
B&SSBC(12x60; 15x75) = (15/12)^2 * (60/75)^2 = 1.5625 * 0.64 = 1.000
OLD UPDATE (after buying the 12x60 binoculars, but before I bought the 8x42 binoculars):
Well, my calculations have been confirmed – my new 12x60 binoculars are clearly better than my old 8x30 binoculars. I live in a block of flats in the middle of a large city where the “light pollution” is big, so my first comparison had to be based on the brightest objects of the night sky. You can check light pollution at your own location here:
https://www.lightpollutionmap.info/
I compared my binoculars when the night became truly dark, so after the end of astronomical twilight:
I compared my binoculars during the night from 29 to 30 July 2020. At my location that astronomical night lasted from 11:55 pm till 2:18 am. Below there is a screenshot of the page:
https://sunrise-sunset.org/
from July 2020 set for my location.
Please notice that at my location the “astronomical white nights” ended just 8 days earlier! What a coincidence. During the “astronomical white nights” the night-sky is never fully dark (because the Sun is too little below the horizon and the astronomical twilight never ends), so any night observations (even without any light pollution) are worse by definition.
On 30 July 2020 I could see with the naked eye two planets: Jupiter and Saturn. Please notice that usually you don't have to wait until the end of the astronomical twilight to see these planets. You can check what you can see at your own location at different times at this site:
https://stellarium-web.org/
HOWEVER this site assumes that there is little light pollution. It's still useful in the middle of the city (with big light pollution), because at least you know in what direction to look in order to check if you can see a particular star or planet.
My “balcony astronomical observatory” is terrible, BUT my new 12x60 binoculars still enabled me to see 3 moons of Jupiter without any problems! Actually there were four moons, but two of them were so close to each other (on the night sky) that I couldn't see them separately. On the screenshot below there is also the moon Amalthea, but it's NOT a Galilean moon – I had to make a big close-up to show you that there was another dot next to the moon Io – it was the moon Europa (in my 12x60 binoculars Jupiter was ONLY a DOT, but larger and brighter than its moons):
My old 8x30 binoculars were not enough to see the moons of Jupiter under such circumstances. And in my new 30x50 spotting scope I could barely see one moon of Jupiter because everything was very dark (and also because I couldn't get a totally steady vision even with a mini tripod). It proves that the most important thing is a proper combination of magnification and brightness, not magnification or brightness alone!
Please notice that using ANY kind of binoculars should enable you to see more stars than with the naked eye. It's incredible feeling, even in the middle of a big city with big light pollution – you look at the night sky only with your own eyes and you see hardly any stars, then you look through binoculars and suddenly many more stars appear! Wow!
OLD UPDATE #2:
Last night we (me and my children) went outside our city to watch the stars with lower light pollution. I picked a place with a “Zenith sky brighness” (according to the site lightpollutionmap.info) of 21.05 which was clearly better than what we have in the middle of our city (19.2). Unfortunately it was early in the night, so the mosquitoes weren't “sleeping” and they were constantly attacking us. It was hard to look at the night sky under such circumstances, but it was still worth a try because the difference in the sky brightness was incredible.
Already with the naked eye we could see much more stars AND we could also see the Milky Way (the main part of our own galaxy seen from the “inside”), but only barely. However when I looked at the Milky Way through my new binoculars I was totally amazed – the number of individual stars that I could see was simply unbelievable. My old binoculars made a big difference too, but not as stunning as the new ones.
We also saw several meteors of the Perseids – meteors from the Perseid meteor shower that is currently “active”. However, because of mosquitoes in the future I will focus on meteor showers that are visible in fall or winter: Draconids, Orionids, Leonids, Geminids, Ursids and Quadrantids.
We (me and my daughter) also saw another galaxy! Wow! It was the Andromeda Galaxy that can theoretically be seen with the naked eye as a blurred dot, but I myself had to use binoculars to see it at all, even outside the city. Please, notice that in binoculars you still can't see the “classic shape” of the galaxy, but rather a “cloud of light” that is clearly something different from the stars that are simply dots. We could see the galaxy also in my old binoculars, but the “cloud of light” was smaller. Either way it looked like this:
I had trouble to locate the galaxy on the night sky because I had been sure that I would spot it with the naked eye, so I didn't precisely memorize the stars around it. I only new the general direction at which I should be looking. It took me 15 minutes to locate the galaxy, but now I know how to find it even in the middle of my city. Yes! You can see the Andromeda Galaxy in 12x60 binoculars even in a large city with relatively big light pollution. I didn't try it with my old binoculars so I have no idea if this is possible with weak binoculars, but you can try it yourself. The only thing to do is to find a place without any bright lanterns close by, so you can see the crucial stars. It goes like this (to simulate big light pollution I used the site Stellarium but at an early hour):
1. Find the Plough / the Big Dipper / the Big Wagon.
2. Find the Ursa Minor / the Little Dipper / the Little Wagon.
3. To the right of them and a little down there is a clear triangle of stars.
4. Extend the bottom line of this triangle by a little more than 100% and a little below this line there is the Andromeda Galaxy!
Click to enlarge!
MOST RECENT UPDATE – PART 3:
Later I bought 8x42 binoculars and I LOVE them! The magnification is the same as in 8x30 binoculars, but they are 96% brighter! In other words: they are almost twice as bright!
B&SSBC(8x42; 8x30) = (8/8)^2 * (42/30)^2 = 1.96
I do not own 10x42 binoculars, but according to my formula the 8x42 binoculars are brighter by 56%:
B&SSBC(8x42; 10x42) = (10/8)^2 * (42/42)^2 = 1.5625 * 1 = 1.5625
I actually prefer the 8x42 binoculars to the 12x60 binoculars simply because they are much smaller and much lighter. In fact I consider the 8x42 binoculars as the most universal type of binoculars – they have very bright and wide view, they have good enough magnification and they are easy to handle by hand (without a tripod). Perfect!
I described many interesting things about binoculars in general here:
Most universal types of binoculars
Please notice that my formula can be even used to compare binoculars with telescopes! Let’s compare 12x60 binoculars to a telescope with 70mm aperture combined with eyepieces that give the magnifications 22x and 70x.
EBC(12x60; 22x70) = (22/12)^2 * (60/70)^2 = 2.4694
EBC(22x70; 12x60) = 1 / 2.4694 = 0.4050
EBC(12x60; 70x70) = (70/12)^2 * (60/70)^2 = 25.0000
EBC(70x70; 12x60) = 1 / 25.0000 = 0.0400
Again, the results are consistent with my experience – I could see the M13 in relatively big light pollution in my 12x60 binoculars and in my small telescope with the magnification 22x (the drop in brightness was “only” 60%), but I couldn’t see it at all in my telescope with the magnification 70x (the drop in brightness was 96%).
Pleas notice that just by increasing the magnification in ANY telescope from 22x to 70x the brightness drops by 90% (relatively to the initial brightness).
EBC(70xA; 22xA) = (22/70)^2 * (A/A)^2 = (22/70)^2 * 1 = 0.0988
Verification (“in steps”):
EBC(70x70; 22x70) * EBC(22x70; 12x60) = 0.0988 * 0.4050 = 0.0400 = EBC(70x70; 12x60)
In the most recent update I have made some changes and I also added new content, based on my additional experience. A year ago I bought a telescope and after some time I realised that the formula described in the present post is useful not only for comparing binoculars and/or spotting scopes, but also for comparing telescopes with particulars eyepieces.
I “discovered” a very interesting thing that can be helpful while deciding what kind of observing equipment to buy.
I have had 8x30 binoculars for a very long time, but recently I decided to buy something with better magnification. I had an opportunity to buy a 30x50 spotting scope for a very low price and I did it. When I compared these two observing tools after getting home I got very surprised.
In most cases while using the 30x50 spotting scope I was able to distinguish only marginally more details than with the 8x30 binoculars! Why? Because everything was much DARKER in the spotting scope and things that were not bright enough were hard to see at all, even though they were bigger.
MOST RECENT UPDATE – PART 1:
For some people it's an ever-going debate what is more important magnification (8x vs. 30x) or aperture (30 vs. 50), but the truth is that aperture on its own is meaningless – your equipment can't improve your own eyes. Looking through a telescope without any magnification would be like looking through some kind of tube. The bigger the aperture the bigger the tube. Would that improve anything? Obviously not.
The naked eye “works at your maximum aperture”, but you can't see things like the rings of Saturn with the naked eye. Well, you can't see them even in binoculars, but they are obvious already in a small telescope (magnification 70x is more than enough to see them). It's also consistent with the fact that it's better to use any kind of binoculars (any kind of magnification) instead of looking at stars with the naked eye (without any magnification).
So, to see more details you need magnification, no doubt about it. This fact alone decides that magnification is more important overall, BUT you have to increase aperture to PREVENT the view from getting too dark (bigger magnification => smaller exit pupil and darker view). And this is exactly what was missing in my 30x50 spotting scope – the magnification was good, but the aperture wasn't up to the task.
As far as binoculars are concerned the brightness is VERY important because it makes the view more “fun”. I bought and compared 8x42 and 10x42 monoculars side by side and I have to say that I can see a little more details and a few more stars (in a particular field of view) in the 10x42 monocular, HOWEVER it feels as if these “more details and more stars” can be seen as a result of “work” rather than “fun”:
1) the field of view is clearly narrower in the 10x42 monocular than in the 8x42 monocular,
2) the image is a little more shaky in the 10x42 monocular than in the 8x42 monocular,
3) the image is clearly darker in the 10x42 monocular than in the 8x42 monocular.
For most people a little more details and a few more stars (in a particular field of view) would not be enough to compensate for the less enjoyable image.
END OF MOST RECENT UPDATE – PART 1.
The observed difference in brightness can be calculated from the above numbers (“8x30” and “30x50”). Obviously we have to ASSUME that everything else is equal. The first number 8x (or 30x) represents magnification or “power” – how many times bigger the observed object appears. The second number 30 (or 50) is aperture – the diameter of each of the objective lenses (the lenses furthest from your eye), given in millimetres.
Let's start with the aperture (the second part of the final formula), because it's more natural. The bigger the aperture – the more light “goes into” the observing tool, so everything should be brighter. The amount of light “going into” the observing tool depends on the AREA of the objective lenses. Let's calculate the respective “going-in” areas:
1) …x30 “going-in” area = PI * R^2 = PI * (30/2)^2 = 3.1416 * 225 = 706.86
2) …x50 “going-in” area = PI * R^2 = PI * (50/2)^2 = 3.1416 * 625 = 1963.5
So if everything else were equal then the brightness of the …x30 observing tool would be 0.36 times of the brightness of the …x50 observing tool (706.86 / 1963.5). The value below 1 means that the …x30 observing tool would be DARKER than the …x50 observing tool. In other words the …x50 observing tool would be 2.7778 times brighter than the …x30 observing tool (1 / 0.36 = 1963.5 / 706.86).
The difference in brightness caused by magnification (“power”) is much more difficult to imagine, but one visual example should be enough to understand. Please remember that this example is NOT about focus and NOT about colours, but about the AMOUNT of light REFLECTED from the observed object that reaches the observing tool. In other words: the smaller objects reflect less light that can be magnified by the observing tool. Again, it's all about areas and again the bigger area improves the brightness, but this time the area is the biggest when the number (magnification) is the smallest!
To make my job easier I drew squares instead of circles, but the idea is clear anyway. The side of all pictures is 480 pixels long. The side of the bigger square is 60 pixels long (magnification of 8x…) and the side of the smaller square is 16 pixels long (magnification of 30x…). The area of the bigger square is 3600 square pixels (60x60) and the area of the smaller square is 256 square pixels (16x16).
As you can see on the last picture there are LESS “pixels of light” stretched (magnified) and this is why the bigger magnification is DARKER.
In reality we can't calculate any REAL areas because in real life there are no pixels to count and we don't know how far away the observed object is. All we can do is to calculate “visual” areas of the two magnifications relatively to each other. Obviously they have to be calculated as circles, not squares.
Assuming that the diameter of the whole visible area is X, then the diameter of the bigger circle (magnification of 8x…) is X/8 and the diameter of the smaller circle (magnification of 30x…) is X/30:
1) 8x… “visual” area = PI * R^2 = PI * ((X/8)/2)^2 = 3.1416 * X^2 / 16^2 = X^2 * 0.012271875
2) 30x… “visual” area = PI * R^2 = PI * ((X/30)/2)^2 = 3.1416 * X^2 / 60^2 = X^2 * 0.000872667
So if everything else were equal then the 8x… observing tool would be 14.0625 times brighter than the 30x… observing tool ((X^2 * 0.012271875) / (X^2 * 0.000872667)). This is exactly the same value as in the example above (3600/256 = 14.0625).
Now we have to combine these two results:
1) if everything else were equal then the brightness of the …x30 observing tool would be 0.36 times of the brightness of the …x50 observing tool,
2) if everything else were equal then the 8x… observing tool would be 14.0625 times brighter than the 30x… observing tool.
We have to simply multiply these two values:
0.36 * 14.0625 = 5.0625
The final value is above 1, so the 8x30 observing tool is 5.0625 times brighter than the 30x50 observing tool. This value explains why everything is much DARKER in my spotting scope and things that are not bright enough are hard to see at all, even though they are bigger than in my binoculars.
Let's simplify the overall formula as much as possible (using also the more natural order):
B&SSBC – Binoculars and Spotting Scopes Brightness Comparison
B&SSBC(A1xA2; B1xB2) = (B1/A1)^2 * (A2/B2)^2
For example:
B&SSBC(8x30; 30x50) = (30/8)^2 * (30/50)^2 = 14.0625 * 0.36 = 5.0625
MOST RECENT UPDATE – PART 2:
My formula works also for telescopes because it’s just a different (greatly simplified) way of comparing exit pupil areas. Below there is my formula with a better (general) name and less confusing “letters”.
EBC – equipment brightness comparison
M – magnification
A – aperture
EBC(M1xA1; M2xA2) = (M2/M1)^2 * (A1/A2)^2
Calculations for comparing exit pupil areas (EPA):
area = Pi * R^2
R = exit pupil/2
exit pupil = A/M
EPA = Pi*R^2 = Pi * (exit pupil/2)^2 = Pi * ((A/M)/2)^2 = Pi * (A/M)^2 * (1/2)^2 = Pi * (A/M * A/M) * 1/4 = Pi * A^2/M^2 * 1/4
EPA1/EPA2 = (Pi * A1^2/M1^2 * 1/4) / (Pi * A2^2/M2^2 * 1/4) = (A1^2/M1^2) / (A2^2/M2^2) = (A1^2/M1^2) * (M2^2/A2^2) = M2^2/M1^2 * A1^2/A2^2 = (M2/M1)^2 * (A1/A2)^2
END OF MOST RECENT UPDATE – PART 2.
The second problem with the 30x50 spotting scope is the fact that it's very hard to use by hand (without a tripod) – very distant observed objects are “jumping” all over the view because you can't keep your hands perfectly steady. For this very reason I ordered another pair of binoculars, this time 12x60 binoculars. Let's compare them to my old binoculars and my new spotting scope:
B&SSBC(12x60; 8x30) = (8/12)^2 * (60/30)^2 = 0.444444 * 4 = 1.777778
B&SSBC(12x60; 30x50) = (30/12)^2 * (60/50)^2 = 6.25 * 1.44 = 9.0000
Now, this is what I call an improvement over my old binoculars – in my new binoculars everything should be larger by 50% ((12-8)/8) AND the brightness should be better by 77%! Both these things combined should make a HUGE difference. We'll see (I will update this post as soon as the my new binoculars arrive and I verify it in reality).
Please notice that B&SSBC values can be calculated is steps:
B&SSBC(12x60; 30x50) = B&SSBC(12x60; 8x30) * B&SSBC(8x30; 30x50) = 1.777778 * 5.0625 = 9.0000
When I was searching various Internet forums about binoculars and spotting scopes I found many suggestions that the 10x50 binoculars are optimal, so let's compare them to the 12x60 binoculars I ordered:
B&SSBC(12x60; 10x50) = (10/12)^2 * (60/50)^2 = 0.6944444 * 1.44 = 1.0000
B&SSBC(10x50; 12x60) = (12/10)^2 * (50/60)^2 = 1.44 * 0.6944444 = 1.0000
EXACTLY the same brightness! So, in my opinion, I ordered the better binoculars – with the same brightness I should be able to see everything bigger by 20%. Using the 12x60 binoculars by hand (without a tripod) should be much easier than using my 30x50 spotting scope by hand, so I should have no problem at all to use them by hand.
On the Internet forums there are many comparisons between 10x50 binoculars and 15x70 binoculars, so let's verify them with my formula:
B&SSBC(10x50; 15x70) = (15/10)^2 * (50/70)^2 = 2.25 * 0.5102 = 1.148
B&SSBC(12x60; 15x70) = (15/12)^2 * (60/70)^2 = 1.5625 * 0.73469 = 1.148
So, 10x50 and 12x60 binoculars should be brighter by 14.8% than 15x70 binoculars. Not that big of a difference, but 15x70 binoculars are much bigger, especially when compared to the 10x50 binoculars AND the bigger magnification makes them harder to use by hand (without a tripod). On the other hand everything will be 50% bigger in the 15x70 binoculars when compared to the 10x50 binoculars, so it's a real toss up. HOWEVER in case of the 12x60 binoculars everything will be only 25% bigger in the 15x70 binoculars, so again the 12x60 binoculars seem like a perfect compromise to me.
Are the 10x50 and 12x60 binoculars the best as far as brightness is concerned? No, they are not! From the binoculars that are usually available there are 8x56 and 9x63 binoculars that are almost TWICE (!!!) as bright, BUT there is a catch (see my comments below calculations):
B&SSBC(8x56; 10x50) = (10/8)^2 * (56/50)^2 = 1.5625 * 1,2544 = 1.96
B&SSBC(8x56; 12x60) = (12/8)^2 * (56/60)^2 = 2.25 * 0.8711111 = 1.96
B&SSBC(9x63; 10x50) = (10/9)^2 * (63/50)^2 = 1.2345679 * 1.5876 = 1.96
B&SSBC(9x63; 12x60) = (12/9)^2 * (63/60)^2 = 1.777778 * 1.1025 = 1.96
However, there is a crucial difference: these binoculars have Exit Pupil of 7 (56/8 and 63/9), instead of 5 (50/3 and 60/12), which can be bad if you are looking at stars with artificial sources of light nearby – under such circumstances your pupils will be smaller than 7mm, which would mean that some brightness of the binoculars will be lost to your eye. What's worse your pupils are getting smaller with age, so such binoculars are good ONLY for young people. By the way, during a day even young people have pupils smaller than 7mm, but there is so much light then that it's not really important. For these very reasons the 8x56 and 9x63 binoculars are called hunting binoculars rather than astronomical binoculars.
On the side note – one of the differences between binoculars is the type of prisms. BAK4 prisms are usually better on the edges than BK7 prisms, especially when there is little light, BUT there may be some exceptions connected with some other details of the prisms. I am not a specialist, so I can't explain anything about prisms. You can Google it on the Internet.
At the end I would like to point out one thing: if you would like to build binoculars or a spotting scope with 15x magnification and the same brightness as the 10x50 and 12x60 binoculars then they would have to be 15x75 binoculars:
B&SSBC(10x50; 15x75) = (15/10)^2 * (50/75)^2 = 2.25 * 0.44444 = 1.000
B&SSBC(12x60; 15x75) = (15/12)^2 * (60/75)^2 = 1.5625 * 0.64 = 1.000
OLD UPDATE (after buying the 12x60 binoculars, but before I bought the 8x42 binoculars):
Well, my calculations have been confirmed – my new 12x60 binoculars are clearly better than my old 8x30 binoculars. I live in a block of flats in the middle of a large city where the “light pollution” is big, so my first comparison had to be based on the brightest objects of the night sky. You can check light pollution at your own location here:
https://www.lightpollutionmap.info/
I compared my binoculars when the night became truly dark, so after the end of astronomical twilight:
I compared my binoculars during the night from 29 to 30 July 2020. At my location that astronomical night lasted from 11:55 pm till 2:18 am. Below there is a screenshot of the page:
https://sunrise-sunset.org/
from July 2020 set for my location.
Please notice that at my location the “astronomical white nights” ended just 8 days earlier! What a coincidence. During the “astronomical white nights” the night-sky is never fully dark (because the Sun is too little below the horizon and the astronomical twilight never ends), so any night observations (even without any light pollution) are worse by definition.
On 30 July 2020 I could see with the naked eye two planets: Jupiter and Saturn. Please notice that usually you don't have to wait until the end of the astronomical twilight to see these planets. You can check what you can see at your own location at different times at this site:
https://stellarium-web.org/
HOWEVER this site assumes that there is little light pollution. It's still useful in the middle of the city (with big light pollution), because at least you know in what direction to look in order to check if you can see a particular star or planet.
My “balcony astronomical observatory” is terrible, BUT my new 12x60 binoculars still enabled me to see 3 moons of Jupiter without any problems! Actually there were four moons, but two of them were so close to each other (on the night sky) that I couldn't see them separately. On the screenshot below there is also the moon Amalthea, but it's NOT a Galilean moon – I had to make a big close-up to show you that there was another dot next to the moon Io – it was the moon Europa (in my 12x60 binoculars Jupiter was ONLY a DOT, but larger and brighter than its moons):
My old 8x30 binoculars were not enough to see the moons of Jupiter under such circumstances. And in my new 30x50 spotting scope I could barely see one moon of Jupiter because everything was very dark (and also because I couldn't get a totally steady vision even with a mini tripod). It proves that the most important thing is a proper combination of magnification and brightness, not magnification or brightness alone!
Please notice that using ANY kind of binoculars should enable you to see more stars than with the naked eye. It's incredible feeling, even in the middle of a big city with big light pollution – you look at the night sky only with your own eyes and you see hardly any stars, then you look through binoculars and suddenly many more stars appear! Wow!
OLD UPDATE #2:
Last night we (me and my children) went outside our city to watch the stars with lower light pollution. I picked a place with a “Zenith sky brighness” (according to the site lightpollutionmap.info) of 21.05 which was clearly better than what we have in the middle of our city (19.2). Unfortunately it was early in the night, so the mosquitoes weren't “sleeping” and they were constantly attacking us. It was hard to look at the night sky under such circumstances, but it was still worth a try because the difference in the sky brightness was incredible.
Already with the naked eye we could see much more stars AND we could also see the Milky Way (the main part of our own galaxy seen from the “inside”), but only barely. However when I looked at the Milky Way through my new binoculars I was totally amazed – the number of individual stars that I could see was simply unbelievable. My old binoculars made a big difference too, but not as stunning as the new ones.
We also saw several meteors of the Perseids – meteors from the Perseid meteor shower that is currently “active”. However, because of mosquitoes in the future I will focus on meteor showers that are visible in fall or winter: Draconids, Orionids, Leonids, Geminids, Ursids and Quadrantids.
We (me and my daughter) also saw another galaxy! Wow! It was the Andromeda Galaxy that can theoretically be seen with the naked eye as a blurred dot, but I myself had to use binoculars to see it at all, even outside the city. Please, notice that in binoculars you still can't see the “classic shape” of the galaxy, but rather a “cloud of light” that is clearly something different from the stars that are simply dots. We could see the galaxy also in my old binoculars, but the “cloud of light” was smaller. Either way it looked like this:
I had trouble to locate the galaxy on the night sky because I had been sure that I would spot it with the naked eye, so I didn't precisely memorize the stars around it. I only new the general direction at which I should be looking. It took me 15 minutes to locate the galaxy, but now I know how to find it even in the middle of my city. Yes! You can see the Andromeda Galaxy in 12x60 binoculars even in a large city with relatively big light pollution. I didn't try it with my old binoculars so I have no idea if this is possible with weak binoculars, but you can try it yourself. The only thing to do is to find a place without any bright lanterns close by, so you can see the crucial stars. It goes like this (to simulate big light pollution I used the site Stellarium but at an early hour):
1. Find the Plough / the Big Dipper / the Big Wagon.
2. Find the Ursa Minor / the Little Dipper / the Little Wagon.
3. To the right of them and a little down there is a clear triangle of stars.
4. Extend the bottom line of this triangle by a little more than 100% and a little below this line there is the Andromeda Galaxy!
Click to enlarge!
MOST RECENT UPDATE – PART 3:
Later I bought 8x42 binoculars and I LOVE them! The magnification is the same as in 8x30 binoculars, but they are 96% brighter! In other words: they are almost twice as bright!
B&SSBC(8x42; 8x30) = (8/8)^2 * (42/30)^2 = 1.96
I do not own 10x42 binoculars, but according to my formula the 8x42 binoculars are brighter by 56%:
B&SSBC(8x42; 10x42) = (10/8)^2 * (42/42)^2 = 1.5625 * 1 = 1.5625
I actually prefer the 8x42 binoculars to the 12x60 binoculars simply because they are much smaller and much lighter. In fact I consider the 8x42 binoculars as the most universal type of binoculars – they have very bright and wide view, they have good enough magnification and they are easy to handle by hand (without a tripod). Perfect!
I described many interesting things about binoculars in general here:
Most universal types of binoculars
Please notice that my formula can be even used to compare binoculars with telescopes! Let’s compare 12x60 binoculars to a telescope with 70mm aperture combined with eyepieces that give the magnifications 22x and 70x.
EBC(12x60; 22x70) = (22/12)^2 * (60/70)^2 = 2.4694
EBC(22x70; 12x60) = 1 / 2.4694 = 0.4050
EBC(12x60; 70x70) = (70/12)^2 * (60/70)^2 = 25.0000
EBC(70x70; 12x60) = 1 / 25.0000 = 0.0400
Again, the results are consistent with my experience – I could see the M13 in relatively big light pollution in my 12x60 binoculars and in my small telescope with the magnification 22x (the drop in brightness was “only” 60%), but I couldn’t see it at all in my telescope with the magnification 70x (the drop in brightness was 96%).
Pleas notice that just by increasing the magnification in ANY telescope from 22x to 70x the brightness drops by 90% (relatively to the initial brightness).
EBC(70xA; 22xA) = (22/70)^2 * (A/A)^2 = (22/70)^2 * 1 = 0.0988
Verification (“in steps”):
EBC(70x70; 22x70) * EBC(22x70; 12x60) = 0.0988 * 0.4050 = 0.0400 = EBC(70x70; 12x60)
Most universal types of binoculars
(Originally posted on Sunday, 21 February 2021; updated most recently on 24 March 2022)
In the most recent update I have made some changes and I also added new content, based on my additional experience. A year ago I bought a telescope and some things about brightness, aperture and magnification are true also for binoculars. I marked the main changes, but I also made numerous small changes throughout the post.
I described how to compare brightness of observing equipment in this post:
Binoculars and spotting scopes brightness comparison
Please, read it first to understand how I created my formula for Binoculars and Spotting Scopes Brightness Comparison (B&SSBC):
B&SSBC(A1xA2; B1xB2) = (B1/A1)^2 * (A2/B2)^2
MOST RECENT UPDATE – MAIN PART:
My formula works also for telescopes because it’s just a different (greatly simplified) way of comparing exit pupil areas. Below there is my formula with a better (general) name and less confusing “letters”.
EBC – equipment brightness comparison
M – magnification
A – aperture
EBC(M1xA1; M2xA2) = (M2/M1)^2 * (A1/A2)^2
In that post I wrote among other things this: “In most cases while using the 30x50 spotting scope I was able to distinguish only marginally more details than with the 8x30 binoculars! Why? Because everything was much DARKER in the spotting scope and things that were not bright enough were hard to see at all, even though they were bigger.”
For some people it's an ever-going debate what is more important magnification (8x vs. 30x) or aperture (30 vs. 50), but the truth is that aperture on its own is meaningless – your equipment can't improve your own eyes. Looking through a telescope without any magnification would be like looking through some kind of tube. The bigger the aperture the bigger the tube. Would that improve anything? Obviously not.
The naked eye “works at your maximum aperture”, but you can't see things like the rings of Saturn with the naked eye. Well, you can't see them even in binoculars, but they are obvious already in a small telescope (magnification 70x is more than enough to see them). It's also consistent with the fact that it's better to use any kind of binoculars (any kind of magnification) instead of looking at stars with the naked eye (without any magnification).
So, to see more details you need magnification, no doubt about it. This fact alone decides that magnification is more important overall, BUT you have to increase aperture to PREVENT the view from getting too dark (bigger magnification => smaller exit pupil and darker view). And this is exactly what was missing in my 30x50 spotting scope – the magnification was good, but the aperture wasn't up to the task.
END OF MOST RECENT UPDATE – MAIN PART.
Last night I looked at the stars from my “balcony astronomical observatory” that is actually terrible because there is big light pollution. With the naked eye I could see barely any stars. In fact, when I looked through a window before going out onto my balcony, at the Western skies I could see the moon and only ONE “star”. This “star” was actually the planet Mars which I learned later from this awesome site:
https://stellarium-web.org/
When I was looking at stars through my 12x60 binoculars I could see much more stars than with the naked eye. By sheer accident a little above Mars I found the open star cluster Pleiades (which I verified later at the above site).
In my 8x30 binoculars this cluster looked much worse – it was clearly smaller and less stars were visible. In my 30x50 this cluster filled my entire view and I could see more stars than in my 8x30 binoculars, BUT the cluster was very hard to find because of the extremely narrow field of view. And obviously I couldn't do it at all while holding my 30x50 spotting scope by hand, so I had to rest it on my balcony guardrail.
My 12x60 binoculars are a little hard to use by hand (without a tripod) and my arms get tired from using them pretty quickly, but I use them this very way. They are definitely more “operable” than 15x70 binoculars that, by the way, actually have slightly worse brightness!
B&SSBC(15x70; 12x60) = (12/15)^2 * (70/60)^2 = 0.64 * 1.361 = 0.871
A value below 1 means that the 15x70 binoculars are darker than 12x60 binoculars. You can calculate it in opposite order:
B&SSBC(12x60; 15x70) = (15/12)^2 * (60/70)^2 = 1.5625 * 0.73469 = 1.148
Please notice that 0.871 = 1 / 1.148, so the formula is perfect. It can be even used to calculate values in steps:
B&SSBC(A1xA2; C1xC2) = B&SSBC(A1xA2; B1xB2) * B&SSBC(B1xB2; C1xC2).
Unfortunately my wife and my children can’t use 12x60 binoculars by hand, so they have to use my old 8x30 binoculars. Because of my brightness fixation I started to worry that they could see much more and/or much better with slightly different binoculars that should be easy to handle.
B&SSBC(8x42; 8x30) = (8/8)^2 * (42/30)^2 = 1.96
B&SSBC(7x35; 8x30) = (8/7)^2 * (35/30)^2 = 1.778
B&SSBC(10x42; 8x30) = (8/10)^2 * (42/30)^2 = 1.254
These brightness values may suggest that the 8x42 binoculars are the best, but the magnification in the 10x42 binoculars is better by 25%.
Recently I did LOTS of research on the net, spending many hours reading articles and discussion about binoculars on various astronomy forums. I will describe the most interesting findings.
1. Type of prisms.
There are two general types of prisms – porro and roof. Binoculars with porro prisms have a classic look (usually narrower at eyes and much wider at the other end) and binoculars with roof prisms have a compact look (they are almost equally narrow at both ends).
The roof prisms are harder to make (it’s always harder to make things that are more compact), so they are more expensive with the same quality of vision. Moreover they have narrower field of view. Finally the roof prisms are almost never advertised for astronomy. All these reasons combined made me focus on binoculars with porro prisms.
2. Glass type for prisms.
There are two general types of glass for prisms – bak-4 and bk7. The binoculars with bk7 prisms are almost never advertised for astronomy, so I focused on bak-4 prisms.
3. Weight and size.
My 12x60 binoculars weigh 1160g and are 21cm long and I think this is the limit for using them without a tripod by an adult man. For a woman or a child such binoculars are definitely too heavy and too big.
I compared weight of many different binoculars available at online stores. Some of them were surprisingly light, but they all had bk7 prisms OR roof prisms that I already discarded.
Binoculars with bak-4 porro prisms that have big magnification and big aperture are biggest and heaviest. The lightest bak-4 porro 10x50 binoculars that I found weighted 900g and were 18cm long. The lightest bak-4 porro 7x50 binoculars were similar to the lightest bak-4 porro 10x50 binoculars, so it seems that generally the size of aperture defines the weight and the length of binoculars. I think that such binoculars would be still too heavy and to big for my wife and my children.
So that left me with only three main types of binoculars that can be better than my 8x30 binoculars: 10x42, 8x42 and 7x35.
4. Field of view (FOV).
The general rule is that bigger magnification gives a narrower field of view. Just look at the picture below. Yellow squares are magnifications of 7x, 8x and 10x. Green squares are magnifications of 12.2 and 31.1 (I had to draw all lines at whole pixels so the green magnifications are not perfect).
When you look at the smaller squares (bigger magnification) you look through a narrower path, so your field of view is narrower. As simple as that. This general rule can be slightly “bent” by using some technological tricks (using optics with different apparent field of view), but not too much.
Here are magnified squares:
As you can clearly see on the last picture there are LESS “pixels of light” stretched (magnified) and this is why the bigger magnification is DARKER. I included this fact into my formula for brightness.
Some people keep talking about field of view and I almost decided to buy 7x35 binoculars just because of it! For example:
Interesting argument, but some people pointed out that the wider the view the worse the quality of the image at the edges of the view. In other words: What is the point of the wide-view when this view is good only closer to the centre?
Moreover I realised that BIGGER aperture in some cases can make the field of view NARROWER. For example I compared 7x35 and 7x50 binoculars produced by the same company:
the 7x35 binoculars had FOV of 163m/1000m,
the 7x50 binoculars had FOV of 112m/1000m.
To make things even more confusing I've read some old discussions on Internet forums where people were praising WIDE field of view of the 7x50 binoculars, but others were criticising them because of big aberrations on the edges of the wide view. In ONLY one topic I found a short side-topic about why 7x50 can actually have NARROWER field of view than 7x35. And in ONLY one topic someone said that 7x50 have much LESS aberrations than 7x35, but nobody really knew why.
Remember that binoculars are in fact a very complex observing tool and different models can be built differently! Any general rule has to be verified by technical specification for a particular model.
There was one more thing that was bothering me. Some optical specifications of prisms alone make the view wide, WITHOUT any magnification. Just compare photos taken with two different cameras:
In the narrower view you see everything larger WITHOUT applying magnification! It means that in the example above the reverse is true – in CAMERAS the wider view makes everything smaller, so lowers magnification! It means that in wide-view CAMERAS the magnification is BELOW 1.
I had been wondering if wide-view optics in binoculars can lower “original” magnification below 1 and only then the magnification of binoculars would be used. All these reasons combined made me discard 7x35 binoculars.
Fortunately, it's NOT what actually happens, but the concept is quite difficult to grasp. I finally understood it when I updated the point VI. Eyepieces and the field of view in this post:
Easy astronomy for total amateurs
Here's the crucial fragment of that post (examples made for a 70/700 telescope):
“Please, remember that you can open all the pictures in different tabs and switch between the tabs to see the differences better.
1. The same magnification, but different optics.
Normal-view (52 degrees) 25mm eyepiece (magnification: 28x)
NARROW-view (43 degrees) 25mm eyepiece (magnification: 28x)
It's like looking at the same picture, but in the narrow-view you are looking through some kind of tube/tunnel. This “looking through a tunnel” effect is annoying to some people, so total amateurs should rather avoid it.
When the idea is reversed the second picture could be considered as the normal-view and the first picture could be considered as the wide-view. So, a wide-view is like looking through a shorter tube/tunnel.”
There are more examples in that post, but they are about different magnifications.
So, what about the above comparison of different real-life pictures? The problem is that they are compared as if they were PRINTED on photo paper of the same size. HOWEVER in wide-view binoculars and in telescopes with wide-view eyepieces the size of the “circle of view” is bigger, so it's like looking at a wider picture printed on photo paper of a bigger size:
In this example you can see that everything is of the same size, so the magnification in wide-view optics is the same.
In case of telescopes you are given the apparent field of view in degrees (AFOV-deg) of the eyepiece and you can calculate the real field of view in degrees (FOV-deg). On the other hand in binoculars you are given the FOV-deg and you can calculate the AFOV-deg. The formulas are very easy:
FOV-deg = AFOV-deg / magnification
AFOV-deg = FOV-deg * magnification
Sometimes the FOV in binoculars is given in meters at 1000 meters (FOV-m), but you can convert it to FOV-deg without any problems:
FOV-deg = FOV-m * 57/1000
FOV-m = FOV-deg * 1000/57
I call it the “magic number 57”, which gives VERY good approximations. I wrote about this “magic number 57” in this post:
Magic number 57
Let's analyse some real examples of binoculars from the same producer:
Binoculars Nikon Aculon 7x35 (9.3 deg or 163m/1000m):
FOV-deg = 163 * 57/1000 = 9.291
FOV-m = 9.3 * 1000/57 = 163.158
AFOV-deg = 9.3 * 7 = 65.1
Binoculars Nikon Aculon 8x42 (8.0 deg or 140m/1000m):
FOV-deg = 140 * 57/1000 = 7.980
FOV-m = 8.0 * 1000/57 = 140.351
AFOV-deg = 8.0 * 8 = 64.0
Binoculars Nikon Aculon 10x42 (6.0 deg or 105m/1000m):
FOV-deg = 105 * 57/1000 = 5.985
FOV-m = 6.0 * 1000/57 = 105.263
AFOV-deg = 6.0 * 10 = 60.0
Please notice that in most of the standard (non wide-field) eyepieces for telescopes the AFOV is 52 degree, so binoculars have generally wider “circle of view”.
5. Exit pupil vs. magnification vs. aperture.
The size of the exit pupil is aperture/magnification, so for 12x60 binoculars it's 5mm (60mm/12). However, calculating the size of the exit pupil is not enough to understanding its meaning.
On the Internet there are some “examples” for exit pupils that are at the same time helpful and extremely misleading! Here's an example for daytime when human pupil is small:
On one hand it's a good comparison between different exit pupils (during day human exit pupil is small, so generally a small exit pupil of binoculars is not important). HOWEVER it's not the way binoculars really work! What actually happens is shown here:
Totally mind-blowing! Please notice that every point at the exit pupil contains light rays coming from ALL the objects in view! You can verify this fact by looking through any kind of binoculars while covering half of the objective lenses – you will still see the whole view (NOT half of it), but the whole view will be half as bright. Here is a fascinating discussion on this topic:
https://www.cloudynights.com/topic/603397-a-basic-exit-pupil-question/
This quote is awesome: “And on your part, I want to thank you for your honest and concerted effort to understand this confusing issue. I can tell you in the Astromart thread I referenced earlier, members whose names are well known here gave Alan French quite a battle before they finally grasped the concept. At the time, I was merely a bystander...”
Let's back to the importance of the size of the exit pupil. During day some light gathered by binoculars with large exit pupil is simply wasted because human eye pupil is smaller than the exit pupil (because human eye pupil constricts due to sunlight). On the other hand during night or evening human pupil is much larger, so generally it's better to use binoculars with a large exit pupil, so human pupil can gather more light. The more light gathered by the HUMAN EYE PUPIL the brighter the image.
HOWEVER it turns out that in telescopes the exit pupil is usually much smaller than the human eye pupil during night and it still gives good results. You can read about it on the net, but now the crucial question is this: “Does smaller pupil makes sense in binoculars?”
Some people in some cases prefer the smaller exit pupil (like 4mm instead of typical 5mm), but this is very subjective preference AND it depends on the viewing condition, especially on the light pollution. Here are some comments that I found on the net:
“As for binos, I've compared tripod-mounted Canon IS 15x50s against tripod-mounted 10x50s, and there's simply no comparison. I can see *much* fainter objects with the 15x50s. Totally different world. And of course, the increase in number of faint stars is even bigger than the increase in number of faint DSOs.”
“It is astonishing how much better my 10x70 does it's job under a dark mag 6 sky. And yet under a mag 4 sky it doesn't provide much more than what I can see in a 10x50 and certainly doesn't provide anywhere near equal image to my 16x70. In fact, in a series of tests, I found the spread in observed LM between the Fujinon 10x70 and 16x70 much wider in poor skies and it had narrowed considerably under mag 6 skies. It was not a constant delta under all sky conditions. All the reason to make different recommendations for different sky conditions.”
“For astronomy, I prefer 10x42's to 8x42's. They weigh the same, the actual "light gathering" is the same but as Mark says, the greater magnification does show more. 10x42's have a 4.2mm exit pupil, 8x42's a brighter 5.25mm exit pupil but both are bright enough for even dark skies.”
After reading the last comment above I almost bought 10x42 binoculars right away. Fortunately one accidental observation made me realise the importance of brightness and I decided to verify some additional things with my own eyes (see the next point).
6. The eye test and additional calculations.
I “discovered” the crucial thing by sheer accident. While using my 12x60 binoculars I found the Coma Berenices Star Cluster (its best part) and I was stunned! This star cluster is rarely mentioned on the Internet, but it's SPECTACULAR! I was not prepared for what I saw – it was totally a WOW moment! When I looked at it with my 8x30 binoculars there was no such effect. Yes, I saw numerous stars, but they were simply too dim. This fact instantly made me want to buy the 8x42 binoculars (NOT the 10x42 binoculars), because they are much brighter!
B&SSBC(8x42; 10x42) = (10/8)^2 * (42/42)^2 = 1.5625 * 1 = 1.5625
B&SSBC(10x42; 8x42) = (8/10)^2 * (42/42)^2 = 0.64 * 1 = 0.64
I was totally torn, so I decided to verify some things with my own eyes and I bought two different monoculars 10x42 (for me) and 8x42 (for my wife and my children). They both have exactly the same size, so their portability is totally equal. They are definitely much more portable than my 8x30 binoculars. For example I can take my monocular when I go to work because it's small enough to fit into a pocket of my jacket!
By the way: monoculars are MUCH LESS expensive than binoculars because in binoculars there are twice as many prisms and the focusing tool is more complex! Moreover in monoculars you NEVER have to worry about collimation!
After numerous comparisons I have to say that you can see more details and more stars through the 10x42 monocular than through the 8x42 monocular, which is a definite proof that magnification is overall more important than brightness, HOWEVER the difference in the number of additional details and stars is rather small (in a particular field of view). More importantly it feels as if these “more details and more stars” can be seen as a result of “work” rather than “fun”:
1) the field of view is clearly narrower in the 10x42 monocular than in the 8x42 monocular,
2) the image is a little more shaky in the 10x42 monocular than in the 8x42 monocular,
3) the image is clearly darker in the 10x42 monocular than in the 8x42 monocular.
It's all about personal preferences, but all these 3 factors point out that the 8x42 binoculars are more “fun”, because the image is simply more enjoyable overall. For most people a little more details and a few more stars (in a particular field of view) would not be enough to compensate for the less enjoyable image.
Interestingly my 8x30 binoculars are slightly better than either of my monoculars! It's probably because using two eyes is better than using one eye, but it may be also connected with the fact that my monoculars have roof prisms instead of porro prisms. So, a monocular is great mostly because of its extreme portability, but in other regards binoculars are generally better.
I bought 8x42 binoculars and when I compared them with my old 8x30 binoculars I was stunned. The image was MUCH better in my new 8x42 binoculars both during the day and during the night! In my new 8x42 binoculars during the day the view was much more “shiny” and during the night the Coma Berenices Star Cluster (its best part) looked almost as good as in my 12x60 binoculars! Generally all the bright stars look better (more “shiny”) with bigger exit pupil.
Please notice that my new 8x42 binoculars are actually slightly brighter than my 12x60 binoculars:
B&SSBC(8x42; 12x60) = (12/8)^2 * (42/60)^2 = 2.25 * 0.49 = 1.1025
B&SSBC(12x60; 8x42) = (8/12)^2 * (60/42)^2 = 0.44444 * 2.04082 = 0.9070
However, the slightly better brightness of the 8x42 binoculars is overwhelmed by the much bigger magnification of the 12x60 binoculars. On the other hand I can hold the 8x42 binoculars for a much longer time. Moreover the image is definitely less shaky in the 8x42 binoculars, especially when my arms are already a little tired. Obviously the 12x60 binoculars are too big and too heavy to be considered universal.
All of this made me reconsider the value of the 7x35 binoculars. They are smaller than the 8x42 binoculars, but are almost as bright:
B&SSBC(7x35; 8x42) = (8/7)^2 * (35/42)^2 = 1.30612 * 0.69444 = 0.9070
B&SSBC(8x42; 7x35) = (7/8)^2 * (42/35)^2 = 0.76563 * 1.44 = 1.1025
The field of view in the 7x35 is even bigger than in the 8x42 binoculars, so the view should be enjoyable too. The weight of the 7x35 binoculars is lower than the weight of the 8x42 binoculars, but it’s not a big difference (around 10%). The magnification is almost the same, so they are pretty close.
The decisive thing is the fact that the 8x42 binoculars are at the same time brighter and have bigger magnification! The field of view in the 8x42 binoculars is already big enough to be enjoyable and the weight is small enough to hold them by hand for longer periods of time. But the 7x35 binoculars are actually quite close.
I must admit that the 7x35 binoculars should be more “fun” than the 8x30 binoculars, mostly because they are much brighter:
B&SSBC(7x35; 8x30) = (8/7)^2 * (35/30)^2 = 1.30612 * 1.36111 = 1.7778
B&SSBC(8x30; 7x35) = (7/8)^2 * (30/35)^2 = 0.76563 * 0.73469 = 0.5625 = 1/1.7778
Here's a new comment I found on the Internet that fits perfectly to my experience:
“It seems that for handheld binoculars, I even appreciate the subtle difference between a 4 and 5mm exit pupil. Even though my 10x42 will show more detail at long distance, the 8x42 seems a more natural extension of my eye. I think this played a role in designers decisions. And why the 7x35 and 10x50, along with stuff like the Audubon 8.5x44, have been so popular.”
7. The most universal type of binoculars.
The most universal type of binoculars: 8x42 binoculars
The 8x42 binoculars have very bright and wide view, they have good enough magnification and they are easy to handle by hand (without a tripod). Perfect!
8. The second most universal type of binoculars.
Now (after my new observations) this is a much more difficult thing to decide (7x35 vs. 10x42). Let’s compare the brightness:
B&SSBC(7x35; 10x42) = (10/7)^2 * (35/42)^2 = 2.04082 * 0.69444 = 1.4172
B&SSBC(10x42; 7x35) = (7/10)^2 * (42/35)^2 = 0.4900 * 1.4400 = 0.7056
In the 7x35 binoculars the brightness is clearly better, the field of view is clearly bigger and the image is less shaky than in the 10x42 binoculars. The only thing in favour of the 10x42 binoculars is the fact that the magnification is 43% bigger ((10-7)/7). The difference in magnification very significant, so choosing between these two types of binoculars would be a real toss-up.
It means that there is no such thing as the “second most universal type of binoculars”.
Fortunately you don’t have to choose between the 7x35 binoculars and the 10x42 binoculars because you can pick the 8x42 binoculars that are a perfect compromise!
9. Size comparison in pictures.
Here's a picture of all of my “old” observing tools:
Please notice that the monoculars are NOT bigger than my 8x30 binoculars, which can be clearly seen at this re-arranged picture:
And here’s a picture of all of my binoculars, including my 8x42 binoculars:
In the most recent update I have made some changes and I also added new content, based on my additional experience. A year ago I bought a telescope and some things about brightness, aperture and magnification are true also for binoculars. I marked the main changes, but I also made numerous small changes throughout the post.
I described how to compare brightness of observing equipment in this post:
Binoculars and spotting scopes brightness comparison
Please, read it first to understand how I created my formula for Binoculars and Spotting Scopes Brightness Comparison (B&SSBC):
B&SSBC(A1xA2; B1xB2) = (B1/A1)^2 * (A2/B2)^2
MOST RECENT UPDATE – MAIN PART:
My formula works also for telescopes because it’s just a different (greatly simplified) way of comparing exit pupil areas. Below there is my formula with a better (general) name and less confusing “letters”.
EBC – equipment brightness comparison
M – magnification
A – aperture
EBC(M1xA1; M2xA2) = (M2/M1)^2 * (A1/A2)^2
In that post I wrote among other things this: “In most cases while using the 30x50 spotting scope I was able to distinguish only marginally more details than with the 8x30 binoculars! Why? Because everything was much DARKER in the spotting scope and things that were not bright enough were hard to see at all, even though they were bigger.”
For some people it's an ever-going debate what is more important magnification (8x vs. 30x) or aperture (30 vs. 50), but the truth is that aperture on its own is meaningless – your equipment can't improve your own eyes. Looking through a telescope without any magnification would be like looking through some kind of tube. The bigger the aperture the bigger the tube. Would that improve anything? Obviously not.
The naked eye “works at your maximum aperture”, but you can't see things like the rings of Saturn with the naked eye. Well, you can't see them even in binoculars, but they are obvious already in a small telescope (magnification 70x is more than enough to see them). It's also consistent with the fact that it's better to use any kind of binoculars (any kind of magnification) instead of looking at stars with the naked eye (without any magnification).
So, to see more details you need magnification, no doubt about it. This fact alone decides that magnification is more important overall, BUT you have to increase aperture to PREVENT the view from getting too dark (bigger magnification => smaller exit pupil and darker view). And this is exactly what was missing in my 30x50 spotting scope – the magnification was good, but the aperture wasn't up to the task.
END OF MOST RECENT UPDATE – MAIN PART.
Last night I looked at the stars from my “balcony astronomical observatory” that is actually terrible because there is big light pollution. With the naked eye I could see barely any stars. In fact, when I looked through a window before going out onto my balcony, at the Western skies I could see the moon and only ONE “star”. This “star” was actually the planet Mars which I learned later from this awesome site:
https://stellarium-web.org/
When I was looking at stars through my 12x60 binoculars I could see much more stars than with the naked eye. By sheer accident a little above Mars I found the open star cluster Pleiades (which I verified later at the above site).
In my 8x30 binoculars this cluster looked much worse – it was clearly smaller and less stars were visible. In my 30x50 this cluster filled my entire view and I could see more stars than in my 8x30 binoculars, BUT the cluster was very hard to find because of the extremely narrow field of view. And obviously I couldn't do it at all while holding my 30x50 spotting scope by hand, so I had to rest it on my balcony guardrail.
My 12x60 binoculars are a little hard to use by hand (without a tripod) and my arms get tired from using them pretty quickly, but I use them this very way. They are definitely more “operable” than 15x70 binoculars that, by the way, actually have slightly worse brightness!
B&SSBC(15x70; 12x60) = (12/15)^2 * (70/60)^2 = 0.64 * 1.361 = 0.871
A value below 1 means that the 15x70 binoculars are darker than 12x60 binoculars. You can calculate it in opposite order:
B&SSBC(12x60; 15x70) = (15/12)^2 * (60/70)^2 = 1.5625 * 0.73469 = 1.148
Please notice that 0.871 = 1 / 1.148, so the formula is perfect. It can be even used to calculate values in steps:
B&SSBC(A1xA2; C1xC2) = B&SSBC(A1xA2; B1xB2) * B&SSBC(B1xB2; C1xC2).
Unfortunately my wife and my children can’t use 12x60 binoculars by hand, so they have to use my old 8x30 binoculars. Because of my brightness fixation I started to worry that they could see much more and/or much better with slightly different binoculars that should be easy to handle.
B&SSBC(8x42; 8x30) = (8/8)^2 * (42/30)^2 = 1.96
B&SSBC(7x35; 8x30) = (8/7)^2 * (35/30)^2 = 1.778
B&SSBC(10x42; 8x30) = (8/10)^2 * (42/30)^2 = 1.254
These brightness values may suggest that the 8x42 binoculars are the best, but the magnification in the 10x42 binoculars is better by 25%.
Recently I did LOTS of research on the net, spending many hours reading articles and discussion about binoculars on various astronomy forums. I will describe the most interesting findings.
1. Type of prisms.
There are two general types of prisms – porro and roof. Binoculars with porro prisms have a classic look (usually narrower at eyes and much wider at the other end) and binoculars with roof prisms have a compact look (they are almost equally narrow at both ends).
The roof prisms are harder to make (it’s always harder to make things that are more compact), so they are more expensive with the same quality of vision. Moreover they have narrower field of view. Finally the roof prisms are almost never advertised for astronomy. All these reasons combined made me focus on binoculars with porro prisms.
2. Glass type for prisms.
There are two general types of glass for prisms – bak-4 and bk7. The binoculars with bk7 prisms are almost never advertised for astronomy, so I focused on bak-4 prisms.
3. Weight and size.
My 12x60 binoculars weigh 1160g and are 21cm long and I think this is the limit for using them without a tripod by an adult man. For a woman or a child such binoculars are definitely too heavy and too big.
I compared weight of many different binoculars available at online stores. Some of them were surprisingly light, but they all had bk7 prisms OR roof prisms that I already discarded.
Binoculars with bak-4 porro prisms that have big magnification and big aperture are biggest and heaviest. The lightest bak-4 porro 10x50 binoculars that I found weighted 900g and were 18cm long. The lightest bak-4 porro 7x50 binoculars were similar to the lightest bak-4 porro 10x50 binoculars, so it seems that generally the size of aperture defines the weight and the length of binoculars. I think that such binoculars would be still too heavy and to big for my wife and my children.
So that left me with only three main types of binoculars that can be better than my 8x30 binoculars: 10x42, 8x42 and 7x35.
4. Field of view (FOV).
The general rule is that bigger magnification gives a narrower field of view. Just look at the picture below. Yellow squares are magnifications of 7x, 8x and 10x. Green squares are magnifications of 12.2 and 31.1 (I had to draw all lines at whole pixels so the green magnifications are not perfect).
When you look at the smaller squares (bigger magnification) you look through a narrower path, so your field of view is narrower. As simple as that. This general rule can be slightly “bent” by using some technological tricks (using optics with different apparent field of view), but not too much.
Here are magnified squares:
As you can clearly see on the last picture there are LESS “pixels of light” stretched (magnified) and this is why the bigger magnification is DARKER. I included this fact into my formula for brightness.
Some people keep talking about field of view and I almost decided to buy 7x35 binoculars just because of it! For example:
Interesting argument, but some people pointed out that the wider the view the worse the quality of the image at the edges of the view. In other words: What is the point of the wide-view when this view is good only closer to the centre?
Moreover I realised that BIGGER aperture in some cases can make the field of view NARROWER. For example I compared 7x35 and 7x50 binoculars produced by the same company:
the 7x35 binoculars had FOV of 163m/1000m,
the 7x50 binoculars had FOV of 112m/1000m.
To make things even more confusing I've read some old discussions on Internet forums where people were praising WIDE field of view of the 7x50 binoculars, but others were criticising them because of big aberrations on the edges of the wide view. In ONLY one topic I found a short side-topic about why 7x50 can actually have NARROWER field of view than 7x35. And in ONLY one topic someone said that 7x50 have much LESS aberrations than 7x35, but nobody really knew why.
Remember that binoculars are in fact a very complex observing tool and different models can be built differently! Any general rule has to be verified by technical specification for a particular model.
There was one more thing that was bothering me. Some optical specifications of prisms alone make the view wide, WITHOUT any magnification. Just compare photos taken with two different cameras:
In the narrower view you see everything larger WITHOUT applying magnification! It means that in the example above the reverse is true – in CAMERAS the wider view makes everything smaller, so lowers magnification! It means that in wide-view CAMERAS the magnification is BELOW 1.
I had been wondering if wide-view optics in binoculars can lower “original” magnification below 1 and only then the magnification of binoculars would be used. All these reasons combined made me discard 7x35 binoculars.
Fortunately, it's NOT what actually happens, but the concept is quite difficult to grasp. I finally understood it when I updated the point VI. Eyepieces and the field of view in this post:
Easy astronomy for total amateurs
Here's the crucial fragment of that post (examples made for a 70/700 telescope):
“Please, remember that you can open all the pictures in different tabs and switch between the tabs to see the differences better.
1. The same magnification, but different optics.
Normal-view (52 degrees) 25mm eyepiece (magnification: 28x)
NARROW-view (43 degrees) 25mm eyepiece (magnification: 28x)
It's like looking at the same picture, but in the narrow-view you are looking through some kind of tube/tunnel. This “looking through a tunnel” effect is annoying to some people, so total amateurs should rather avoid it.
When the idea is reversed the second picture could be considered as the normal-view and the first picture could be considered as the wide-view. So, a wide-view is like looking through a shorter tube/tunnel.”
There are more examples in that post, but they are about different magnifications.
So, what about the above comparison of different real-life pictures? The problem is that they are compared as if they were PRINTED on photo paper of the same size. HOWEVER in wide-view binoculars and in telescopes with wide-view eyepieces the size of the “circle of view” is bigger, so it's like looking at a wider picture printed on photo paper of a bigger size:
In this example you can see that everything is of the same size, so the magnification in wide-view optics is the same.
In case of telescopes you are given the apparent field of view in degrees (AFOV-deg) of the eyepiece and you can calculate the real field of view in degrees (FOV-deg). On the other hand in binoculars you are given the FOV-deg and you can calculate the AFOV-deg. The formulas are very easy:
FOV-deg = AFOV-deg / magnification
AFOV-deg = FOV-deg * magnification
Sometimes the FOV in binoculars is given in meters at 1000 meters (FOV-m), but you can convert it to FOV-deg without any problems:
FOV-deg = FOV-m * 57/1000
FOV-m = FOV-deg * 1000/57
I call it the “magic number 57”, which gives VERY good approximations. I wrote about this “magic number 57” in this post:
Magic number 57
Let's analyse some real examples of binoculars from the same producer:
Binoculars Nikon Aculon 7x35 (9.3 deg or 163m/1000m):
FOV-deg = 163 * 57/1000 = 9.291
FOV-m = 9.3 * 1000/57 = 163.158
AFOV-deg = 9.3 * 7 = 65.1
Binoculars Nikon Aculon 8x42 (8.0 deg or 140m/1000m):
FOV-deg = 140 * 57/1000 = 7.980
FOV-m = 8.0 * 1000/57 = 140.351
AFOV-deg = 8.0 * 8 = 64.0
Binoculars Nikon Aculon 10x42 (6.0 deg or 105m/1000m):
FOV-deg = 105 * 57/1000 = 5.985
FOV-m = 6.0 * 1000/57 = 105.263
AFOV-deg = 6.0 * 10 = 60.0
Please notice that in most of the standard (non wide-field) eyepieces for telescopes the AFOV is 52 degree, so binoculars have generally wider “circle of view”.
5. Exit pupil vs. magnification vs. aperture.
The size of the exit pupil is aperture/magnification, so for 12x60 binoculars it's 5mm (60mm/12). However, calculating the size of the exit pupil is not enough to understanding its meaning.
On the Internet there are some “examples” for exit pupils that are at the same time helpful and extremely misleading! Here's an example for daytime when human pupil is small:
On one hand it's a good comparison between different exit pupils (during day human exit pupil is small, so generally a small exit pupil of binoculars is not important). HOWEVER it's not the way binoculars really work! What actually happens is shown here:
Totally mind-blowing! Please notice that every point at the exit pupil contains light rays coming from ALL the objects in view! You can verify this fact by looking through any kind of binoculars while covering half of the objective lenses – you will still see the whole view (NOT half of it), but the whole view will be half as bright. Here is a fascinating discussion on this topic:
https://www.cloudynights.com/topic/603397-a-basic-exit-pupil-question/
This quote is awesome: “And on your part, I want to thank you for your honest and concerted effort to understand this confusing issue. I can tell you in the Astromart thread I referenced earlier, members whose names are well known here gave Alan French quite a battle before they finally grasped the concept. At the time, I was merely a bystander...”
Let's back to the importance of the size of the exit pupil. During day some light gathered by binoculars with large exit pupil is simply wasted because human eye pupil is smaller than the exit pupil (because human eye pupil constricts due to sunlight). On the other hand during night or evening human pupil is much larger, so generally it's better to use binoculars with a large exit pupil, so human pupil can gather more light. The more light gathered by the HUMAN EYE PUPIL the brighter the image.
HOWEVER it turns out that in telescopes the exit pupil is usually much smaller than the human eye pupil during night and it still gives good results. You can read about it on the net, but now the crucial question is this: “Does smaller pupil makes sense in binoculars?”
Some people in some cases prefer the smaller exit pupil (like 4mm instead of typical 5mm), but this is very subjective preference AND it depends on the viewing condition, especially on the light pollution. Here are some comments that I found on the net:
“As for binos, I've compared tripod-mounted Canon IS 15x50s against tripod-mounted 10x50s, and there's simply no comparison. I can see *much* fainter objects with the 15x50s. Totally different world. And of course, the increase in number of faint stars is even bigger than the increase in number of faint DSOs.”
“It is astonishing how much better my 10x70 does it's job under a dark mag 6 sky. And yet under a mag 4 sky it doesn't provide much more than what I can see in a 10x50 and certainly doesn't provide anywhere near equal image to my 16x70. In fact, in a series of tests, I found the spread in observed LM between the Fujinon 10x70 and 16x70 much wider in poor skies and it had narrowed considerably under mag 6 skies. It was not a constant delta under all sky conditions. All the reason to make different recommendations for different sky conditions.”
“For astronomy, I prefer 10x42's to 8x42's. They weigh the same, the actual "light gathering" is the same but as Mark says, the greater magnification does show more. 10x42's have a 4.2mm exit pupil, 8x42's a brighter 5.25mm exit pupil but both are bright enough for even dark skies.”
After reading the last comment above I almost bought 10x42 binoculars right away. Fortunately one accidental observation made me realise the importance of brightness and I decided to verify some additional things with my own eyes (see the next point).
6. The eye test and additional calculations.
I “discovered” the crucial thing by sheer accident. While using my 12x60 binoculars I found the Coma Berenices Star Cluster (its best part) and I was stunned! This star cluster is rarely mentioned on the Internet, but it's SPECTACULAR! I was not prepared for what I saw – it was totally a WOW moment! When I looked at it with my 8x30 binoculars there was no such effect. Yes, I saw numerous stars, but they were simply too dim. This fact instantly made me want to buy the 8x42 binoculars (NOT the 10x42 binoculars), because they are much brighter!
B&SSBC(8x42; 10x42) = (10/8)^2 * (42/42)^2 = 1.5625 * 1 = 1.5625
B&SSBC(10x42; 8x42) = (8/10)^2 * (42/42)^2 = 0.64 * 1 = 0.64
I was totally torn, so I decided to verify some things with my own eyes and I bought two different monoculars 10x42 (for me) and 8x42 (for my wife and my children). They both have exactly the same size, so their portability is totally equal. They are definitely much more portable than my 8x30 binoculars. For example I can take my monocular when I go to work because it's small enough to fit into a pocket of my jacket!
By the way: monoculars are MUCH LESS expensive than binoculars because in binoculars there are twice as many prisms and the focusing tool is more complex! Moreover in monoculars you NEVER have to worry about collimation!
After numerous comparisons I have to say that you can see more details and more stars through the 10x42 monocular than through the 8x42 monocular, which is a definite proof that magnification is overall more important than brightness, HOWEVER the difference in the number of additional details and stars is rather small (in a particular field of view). More importantly it feels as if these “more details and more stars” can be seen as a result of “work” rather than “fun”:
1) the field of view is clearly narrower in the 10x42 monocular than in the 8x42 monocular,
2) the image is a little more shaky in the 10x42 monocular than in the 8x42 monocular,
3) the image is clearly darker in the 10x42 monocular than in the 8x42 monocular.
It's all about personal preferences, but all these 3 factors point out that the 8x42 binoculars are more “fun”, because the image is simply more enjoyable overall. For most people a little more details and a few more stars (in a particular field of view) would not be enough to compensate for the less enjoyable image.
Interestingly my 8x30 binoculars are slightly better than either of my monoculars! It's probably because using two eyes is better than using one eye, but it may be also connected with the fact that my monoculars have roof prisms instead of porro prisms. So, a monocular is great mostly because of its extreme portability, but in other regards binoculars are generally better.
I bought 8x42 binoculars and when I compared them with my old 8x30 binoculars I was stunned. The image was MUCH better in my new 8x42 binoculars both during the day and during the night! In my new 8x42 binoculars during the day the view was much more “shiny” and during the night the Coma Berenices Star Cluster (its best part) looked almost as good as in my 12x60 binoculars! Generally all the bright stars look better (more “shiny”) with bigger exit pupil.
Please notice that my new 8x42 binoculars are actually slightly brighter than my 12x60 binoculars:
B&SSBC(8x42; 12x60) = (12/8)^2 * (42/60)^2 = 2.25 * 0.49 = 1.1025
B&SSBC(12x60; 8x42) = (8/12)^2 * (60/42)^2 = 0.44444 * 2.04082 = 0.9070
However, the slightly better brightness of the 8x42 binoculars is overwhelmed by the much bigger magnification of the 12x60 binoculars. On the other hand I can hold the 8x42 binoculars for a much longer time. Moreover the image is definitely less shaky in the 8x42 binoculars, especially when my arms are already a little tired. Obviously the 12x60 binoculars are too big and too heavy to be considered universal.
All of this made me reconsider the value of the 7x35 binoculars. They are smaller than the 8x42 binoculars, but are almost as bright:
B&SSBC(7x35; 8x42) = (8/7)^2 * (35/42)^2 = 1.30612 * 0.69444 = 0.9070
B&SSBC(8x42; 7x35) = (7/8)^2 * (42/35)^2 = 0.76563 * 1.44 = 1.1025
The field of view in the 7x35 is even bigger than in the 8x42 binoculars, so the view should be enjoyable too. The weight of the 7x35 binoculars is lower than the weight of the 8x42 binoculars, but it’s not a big difference (around 10%). The magnification is almost the same, so they are pretty close.
The decisive thing is the fact that the 8x42 binoculars are at the same time brighter and have bigger magnification! The field of view in the 8x42 binoculars is already big enough to be enjoyable and the weight is small enough to hold them by hand for longer periods of time. But the 7x35 binoculars are actually quite close.
I must admit that the 7x35 binoculars should be more “fun” than the 8x30 binoculars, mostly because they are much brighter:
B&SSBC(7x35; 8x30) = (8/7)^2 * (35/30)^2 = 1.30612 * 1.36111 = 1.7778
B&SSBC(8x30; 7x35) = (7/8)^2 * (30/35)^2 = 0.76563 * 0.73469 = 0.5625 = 1/1.7778
Here's a new comment I found on the Internet that fits perfectly to my experience:
“It seems that for handheld binoculars, I even appreciate the subtle difference between a 4 and 5mm exit pupil. Even though my 10x42 will show more detail at long distance, the 8x42 seems a more natural extension of my eye. I think this played a role in designers decisions. And why the 7x35 and 10x50, along with stuff like the Audubon 8.5x44, have been so popular.”
7. The most universal type of binoculars.
The most universal type of binoculars: 8x42 binoculars
The 8x42 binoculars have very bright and wide view, they have good enough magnification and they are easy to handle by hand (without a tripod). Perfect!
8. The second most universal type of binoculars.
Now (after my new observations) this is a much more difficult thing to decide (7x35 vs. 10x42). Let’s compare the brightness:
B&SSBC(7x35; 10x42) = (10/7)^2 * (35/42)^2 = 2.04082 * 0.69444 = 1.4172
B&SSBC(10x42; 7x35) = (7/10)^2 * (42/35)^2 = 0.4900 * 1.4400 = 0.7056
In the 7x35 binoculars the brightness is clearly better, the field of view is clearly bigger and the image is less shaky than in the 10x42 binoculars. The only thing in favour of the 10x42 binoculars is the fact that the magnification is 43% bigger ((10-7)/7). The difference in magnification very significant, so choosing between these two types of binoculars would be a real toss-up.
It means that there is no such thing as the “second most universal type of binoculars”.
Fortunately you don’t have to choose between the 7x35 binoculars and the 10x42 binoculars because you can pick the 8x42 binoculars that are a perfect compromise!
9. Size comparison in pictures.
Here's a picture of all of my “old” observing tools:
Please notice that the monoculars are NOT bigger than my 8x30 binoculars, which can be clearly seen at this re-arranged picture:
And here’s a picture of all of my binoculars, including my 8x42 binoculars:
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