If this is true, why does the Orion Nebula (choosing an extended object to avoid discussion of point-like stars) look much brighter in my 10x30s than with my naked eye? I always thought - because a 30 mm aperture collects 302 / 72 (18 times) as much light as an eye that is open to 7 mm. On the other hand, that light is concentrated in a ~3 mm diameter patch on the retina. Is Nikon saying that this reduced area of illumination (compared with the full opening of 7 mm) cancels out the 18 times greater light gathering? Even if that makes any sense, it isn't exactly true arithmetically - 302 / 72 is not equal to 72 / 32 . And common sense suggests it must be wrong.
This is complicated and sometimes counterintuitive. I will try to explain it the best I can.
- The exit pupil is the beam of light leaving the eyepiece that you look at. If you look at the eyepiece lens from a distance, you can see the exit pupil as a bright circle that is actually an image of what the objective sees. As Nikon says, the diameter of the exit pupil is equal to the aperture divided by the magnification.
You can verify this by making a ring with your thumb and forefinger and placing it in front of one of the objectives, as you make the ring smaller, you can see the exit pupil get smaller.
- The exit pupil contains the entire image regardless of the exit pupil. The entire field of view of the retina is illuminated, not just a 3mm diameter, regardless of the diameter of the exit pupil. When your pupil contracts, the image becomes dimmer but you still see the same image.
You can repeat the above experiment but this time look through one side of the binoculars while forming the ring with your thumb and forefinger in front of the objective. As you make the ring smaller, the field of view remains the same but the image becomes dimmer and dimmer.
If your pupil were open to 7mm, and you had 10x70 binoculars, then the 7mm exit pupil would fill your pupil and the image would be as bright as the night sky. As you constrict the ring to 50mm in diameter, 40mm, 30mm, the image dims because you are collecting less light but that light is being spread over the same area.
The image brightness of a 3mm exit pupil compared to a 7mm exit pupil is related to the area, the 10x30s are 9/49 = 18.4% the brightness of 10x70s.
- It is important to understand the concept of brightness is surface brightness, that's photons per unit area. The 10x30s capture (30/7)2 = 18.4x the light but it is magnified 10 times so it is spread out over 102 = 100 times the area. Thus each retinal cell receives 18.4/100 = 18.4% of the light.
- Why the Orion nebula appears brighter: This has to do with the workings of eye/brain. A camera would see the image of Orion in the binoculars as being 10x larger in diameter but about 1/5th as bright.
The eye doesn't work that way. As long as the image is sufficiently bright, the eye is primarily a contrast detector, Contrast is the ratio of the brightnesess in an image. When you magnify the image, the object itself dims but so does the background sky and it is all in proportion so magnifying an image does not change the contrast, it just makes it dimmer. But the bigger image shows more detail and the eye/brain interpret that as being brighter.
Imagine looking at Orion in a 300mm telescope at 100x. Your binoculars show a much more detailed image of Orion because the image is 10 times larger even though it's about 1/5th the brigthtness. With a 300mm telescope at 100x, the image is 10 times larger than in the binoculars and of equal brightness.
This is a complex subject and the concepts are difficult to grasp. Hopefully you can perform the experiments I outlined and you can get some sort of a handle on things.