Ratio of received light through lens to the human eye

[medwatt]

Hello,

I know that the larger the aperture the more light it can focus in thereby making faint objects less faint. I read somewhere where a guy said that a 10x50 bino will grab up to 100 times more light than an ordinary human eye. I tried some analysis of my own and wonder if this is the way the ratio is calculated.

During the day :

2 x Pupil Diameter = 2 x 3mm = 6mm

2 x binos Diamter = 2 x 50mm = 100mm

Assuming that the light width is proportional to power, P :

Pupil Power = 6k

Bino Power = 100k

Since the exit pupil diameter is 5mm then the intensity of the light is increases by that factor since all the light from the objective lens is now through the ocular lens : Hence Bino Power = 500k.

Ratio = 500/6 = 83

Therefore a 10x50 bino is 83 times more powerful than an ordinary human eye.

Also a 15x70 is (653/6)  is 108 times more powerful.

Therefore a 15x70 is just 1.3 times more powerful than 10x50 bino.

Please tell me if this is the way they calculate such things.

[Langy]

Not sure that the 10x50 will actually capture more than 100 times more light than the human eye. The human eye has a massive FOV therefore no telescope or binoculars will even match the human eye for capturing light.

[ronin]

Title appears wrong, the amount of light received is not dependant on the magnification, the intensity of the image is but the amount is not.

The ratio of gathered light through the 15x70 - they have a diameter of 70mm, the 10x50 have a 50mm dia so the ration of collected light is simply 70/50 squared, as it is a ratio forget the 0's and it is 7/5 squared or 1.4 squared or 1.96 times as much light is gathered. Don't even need a calculator for that bit.

The image in the 15x70's should be 0.87 times the brightness of the image in the 10x50, so actually dimmer, meaning you can see more in the 10x50's then the 15x70's. But the lure of 15x seems to override this simple calculation. Very easy to do as you simply divide the aperture by the magnification and whichever has the bigger value is the brighter. That is why 8x42's are so popular, small, light, easy to use and brighter.

[AlexB67]

Form your post it sounds like something that is known as the brightness factor is what you are after, which is given by

((aperture / eye pupil size) / Magnfication)^2

or since magnification is aperture / exit pupil size you can look at it another way. That makes physical sense in the following way, since light gathering is proportional to area, hence all the other terms including pi cancel, so that is what you are left with.

As an example, if your eyepupil is the same size as the exit pupil, the object would appear as bright as it would to the naked eye, but at that magnification as seen in the scope.  In practice this is not quite true since there is light loss, it would actually be less bright, but the concept is useful all the same.  You could define an effective brigthness factor that takes that into account such things as transmission loss at the eyepiece and other optics but for a direct comparison as a theoretical brightness concept this is fine.

Have a look at this page

http://www.stargazing.net/naa/scopemath.htm

and the explanations on there  and play with it.  Of course all I said applies to  monocular vision, but for bins the principles should be the same per eye.

[AlexB67]

Something else I meant to say, and  a useful rule of thumb. when thinking about a physical quantity such as power, it is a scalar quantity, that may all smell like a bit of academic goo, but it is very useful concept. A diameter such as aperture with dimension of length is a vector,  it can have a positive or negative sign associated with it as well and a direction. Something like power or light gathering power cannot be a vector quantity. This means when figuring things out on the back of an envelope you would know there is something wrong, the squares in the equation takes care of that and it hints at a few things whether you are on the right track or not.

All that math is useful for something, but often forgotten 

HTH