Question

on this page: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/interf.html#c1
Why is the path length difference at the start multiplied by n, shouldnt it be S=AB+BC-AD?

Answer 1

because the velocity of light is different in the medium ... and n is refractive index.

Answer 2

To elaborate a little bit.... The velocity of light changes when you enter the medium. Since for a light wave, the velocity is equal to the frequency times the wavelength, you might ask whether this is reflected in a change of frequency, wavelength or both. However, because the energy carried by the wave is proportional to the frequency and should be unchanged, you may conclude that the wavelength is decreased by a factor of "n". When you talk about optical path length, the essence of what you're trying to find is the number of wavelengths traveled.

Let's say the wavelength of a particular light wave happens to be 1 meter, and I have a plate in which n = 2. I simultaneously shine two beams, one which misses the plate and another which goes through it. Now, I ask whether the beams end up in phase or out of phase.