Why is it that for two pairs of binoculars, with equal aperture, the one with smaller magnification has larger exit pupil and results in brighter images? If I understand correctly, the aperture determines the amount of light collected, meaning both pairs of binoculars should collect the same light. Moreover, the one withe smaller magnification, giving a larger exit pupil should spread the light over a larger area. What is it that I am missing here? I cannot find this explained anywhere.
1 Answer
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The aperture of the objective lens controls the amount of light passing though the binoculars it does not affect the size of final image on the retina.
If you use a pair of 7 x 50 binoculars then the exit pupil has a diameter of $50/7 \approx 7 \,\rm mm$ which is the "nominal" diameter of the pupil of an eye, ie all the light which enters the objective lens ends up on the retina of the eye.
If the eye pupil diameter is $5\,\rm mm$ and the exit pupil is $7 \,\rm mm$ then a significant fraction of the light which passes through the binoculars does not reach the retina and in fact the 7 x 50 binoculars are acting as though they were 7 x 35 binoculars.
A pair of 10 x 50 binoculars with an eye pupil diameter of $5\,\rm mm$ take advantage of the full light-gathering abilities of the binoculars.
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$\begingroup$ I understand what you explain, but it was not the point of my question. My question is why is it that for two scopes with the same aperture (therefore collecting the same amount of light) the one with larger exit pupil will have higher brigthness, considering light is spread over a larger area in the exit pupil $\endgroup$ Commented Jun 23 at 15:16