BTW if your physics prof is dead that means he hasn't seen the new advancements in lens coatings and technology eh?
He did see plenty of single magflouride coatings, and more modern multi-coatings only increase transmissivity by another 9% (that's what Nikon says here:
http://www.maxwell.com.au/photo/nikon/sportoptics/interest/key.html ). He also knew a thing or two about optics, knowledge which some posters here apparently lack.
I read all the talk about the magical
exit pupil but nothing on the more important characteristics relavent to this discussion:
relative brightness and
twilight factor. To compute the Exit Pupil: divide the diameter of the objective lens in millimeters by the power of the scope. To compute Relative Brightness: square the Exit Pupil. An 8mm EP has a relative brightness of 64. An 11mm exit pupil has a RB of 121, twice as bright as the 8mm scope.
Another factor is the
twilight factor. Twilight Factor = square root of (magnification x aperture). The TL factor for our 2x Leupold is 6.3. That for the 4x is 10.6. That's why the 4x appears brighter at twilight, as Greybeard suggests. Both have the same coatings, so that is a non-factor in the physics of the two lens systems.
These characteristics are mathematically derived and anyone can calculate them without measuring instruments. Another effect of the physics of the lenses is very obvious - the more glass in the scope the less light can pass through it. All else equal, the scope with fewer lenses will be brighter. Magic coatings help transmissivity but they are not 100% efficient either - very good coatings are 90-95% efficient, so light is lost through the coatings as well. Nope, coatings are hardly the chief factor in a scope's brightness.