You haven't. We're just talking about different kinds of "brightness". I'm considering surface brightness- photons per unit area. A telescope can't increase that (although it frequently decreases it). You're talking about the total signal- the photon count. As I noted, we can perceive a magnified image with the same surface brightness as apparently brighter because we involve more of the retina. We're getting more signal even though the surface brightness hasn't increased.Nitpicker wrote:Back to telescopes with eyepieces ... Assuming a perfect instrument, I would consider the ratio of the area of the telescope aperture, to the area of the eyepiece exit pupil (especially if well matched to the area of the observer's pupil) to be a good measure of how much brighter objects appear in the telescope, compared with the unaided eye. Simply a measure of the increase in the number of photons per unit time, reaching the retina. So, Chris, where have I gone wrong?
(The surface brightness of the retinal image decreases when the aperture and exit pupil aren't properly matched. No matter how large the aperture, the eye only sees photons collected by a diameter equal to the exit pupil times the magnification. If the exit pupil is larger than the eye, the full aperture isn't being utilized. If the projected aperture (exit pupil times magnification) is larger than the physical aperture, the surface brightness is reduced compared with the naked eye brightness. This is why you can't make a unit magnification telescope that gives you an unmagnified but brighter view. The largest aperture a unit magnification telescope can have is one which is the same size as your eye's pupil. It's also why the Moon will never damage your eye, no matter how large an aperture your telescope has.)