Amount Of Light VS Lens Size ?

[Wedgy]

Is there a formula to compare how much more light I would gain from a larger objective, given all else is equal ? For example a 5x power scope with a 42mm objective(5542 sqmm) compared to a 50mm(7854 sqmm) is ~40% more area and a
56mm(9852 sqmm) is ~78% more area.
Any idea how much more visible light one would gain ? I'm pretty sure it's not a simple surface area calculation, if I even got those right. My knowledge in this area is limited but I'm pretty sure somebody here is a rocket scientist in optics.

And with binoculars how would a set of 10x50mm compare to an 8x50mm or a 7x 50mm, again same brand, lens, etc. only difference being the lens size ?

Please enlighten me.

 

[4xforfun]

Glass quality and lens coating quality have just as much, if not more affect the sheer lens size.

 

[Wedgy]

Yes that's why I said "all else being equal".
Same brand, same power, etc. just size being the only variable.

 

[4xforfun]

Yes that's why I said "all else being equal".
Same brand, same power, etc. just size being the only variable.

OOPS...sorry. My reading skills are EXCELLENT!! My comprehention....not so much. lightbulb

I am not sure about that...I am pretty sure that a 50MM lens is not 40% brighter than a 44. But, as you said, there must be some kind of formula.

 

[Wedgy]

Trying to figure out the benefits of upgrading to a 50mm or 56mm from a 42mm and of a lower magnification pair of binos for bow hunt where I really don't need see very far but the light is very low in a canyon I like to hunt, dropping down to 7x from 10x. I would like to have some type of quantitative measurement other than surface area.

 

[Rich Coyle]

Is there a formula to compare how much more light I would gain from a larger objective, given all else is equal ? For example a 5x power scope with a 42mm objective(5542 sqmm) compared to a 50mm(7854 sqmm) is ~40% more area and a
56mm(9852 sqmm) is ~78% more area.
Any idea how much more visible light one would gain ? I'm pretty sure it's not a simple surface area calculation, if I even got those right. My knowledge in this area is limited but I'm pretty sure somebody here is a rocket scientist in optics.

And with binoculars how would a set of 10x50mm compare to an 8x50mm or a 7x 50mm, again same brand, lens, etc. only difference being the lens size ?

Please enlighten me.

I love to play with optics. I compare them often. Some folks make fun of me for comparing scopes with binoculars. It does not phase me a bit.

I used to have a Minox 13X56. They are really nice bins. They have more than twice the surface area as a Bushnell 6500 4 1/2-30X50 rifle scope. With the 6500 set on 13X in side by side comparison the 6500 lasts two minutes longer on deer antlers in the woods 131 yards away. Then I got some Minox 15X58. With the 6500 set on 15X the Minox 15X58 lasted twelve minutes longer than the 6500 scope.

The 58 are marginally larger and yet more than significantly better in low light. By the way the 13X56 were newer than the 15X58.

 

[lineworker81]

Wedgy i had the same question a few years ago so i searched for an answer. Heres what i came up with. The exit pupil of a scope givin all thing equal is determined by objective divided by magnification. So a 6.5-20x50 scope 50 divided by 6.5 comes up with an exit pupil of 7.7mm. The human pupil will let light in from around 5mm to somewhere around 7mm obviously every eye is not the same. So if all this is correct givin all things equal two exact scopes with only different objectives if the exit pupil is above 7 on both a human wont be able to use the extra light. The larger objective would give a larger field of view but as far as low light performance i dont think it would be seen. Im not an expert at all i just spent alot of time chasing an answer a few years ago. If you google exit pupil vs light transmission you will find alot of reading that will explain it alot better than i can.

 

[Rich Coyle]

The larger objective would give a larger field of view but as far as low light performance i dont think it would be seen.

Actually it's the other end determining larger or smaller field of view. Maybe an expert will chime in and give us the technical information.

 

[918v]

You're not going to see much of a difference in lowlight between 50 and 56mm like you would see between 40 and 56mm where it is quite noticeable. There are several ways of getting better lowlight performance: increase size of objective, decrease magnification, reduce number of lenses in the system, use better coatings. So when comparing scopes take these variables into consideration. Your best bet for lowlight performance is a fixed power scope with a big objective, like 8x56 or 6x42, etc.

 

[Wedgy]

Thanks for the input. A few people PM'd me with some info and I found some reading about exit pupil and as you stated;
----------------------------------------------------------------------------------------------
The pupil of a human eye ranges from about 1.5mm in bright conditions to about 8mm in the dark. If your binoculars' exit pupil diameter is smaller than the pupil of your eye, it's going to seem like you're looking through a peep hole. Bear in mind that as eyes age, they tend to dilate less, so exit pupil becomes more important as the user ages.
Binoculars' exit pupil diameter is determined by dividing the objective by the magnification: so a 10x42 binocular has a 4.2mm exit pupil diameter. That's a generous size, and larger than the pupil of the eye most of the time. But a 10x25 pair of binoculars has an exit pupil of just 2.5mm, which is smaller than the average pupil dilation and will be harder to see through clearly.
--------------------------------------------------------------------------------------
So a set of 7x50 binos would be about as good as it gets for low light(50/7 = 7.15mm exit pupil), given quality glass of course. As everybody knows once you have used quality glass in low light hunting conditions there is no going back. I just wish it wasn't so expensive.

 

[Rifleman513]

As you stated the exit pupil is a good starting point for "low light performance". Also quality starts to play a big role as well. I recently got a second pair of binos. I had been using 10x42's 4.2mm exit pupil. My new ones are 12x50's 4.17mm exit pupil. There is no comparison between the two the higher end 12's are so much better in low light.

With that said, the 4.5-6 avg. pupil size is pretty accurate for most people under most lower light conditions. Finding a high quality optic that falls into these parameters should give you what you are looking for.

 

[FEENIX]

I ran into this and posting it for what it is worth ...

[ame]https://youtu.be/sOdWOylLLF8?t=59[/ame]

This is a bit old (set the bias aside) but I think the explanation is still helpful IMHO.

Cheers!

Ed