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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