I was wondering if someone can clarify the relationship between index of refraction and frequency. I know that when light is entering into a high index of refraction (say air to glass) that the index is increasing, light bends towards the normal, the speed decreases, and wavelength becomes shorter. But what about frequency, is proportional to the index of refraction (as index increases so does frequency), or is it constant throughout the travel of the light? Thank You in advance
The frequency stays constant. It has to stay constant in order for the oscillating electric and magnetic fields on the two sides of the boundary to match up properly at the boundary, at all times. You can see something similar if you tie a light string and a heavier string together, end to end, and send a wave along them. The wave speed and wavelength are different in the two strings, but the frequency is the same, because the ends of the two strings are stuck together so they have to move together at that point.
Thanks jtbell, that cleared things up for me. If you do not mind I have one more question. Say you are looking through a lens with the object on the opposite side, and the particles (p1 and p2) emitted from the object reaches the observer at the same time. Say p1 hits the center of the lens where the center is thicker, and p2 hits top end of lens where the thickness is thiner than the center. So would p1 be faster than p2 in order to reach the observer at the same time, or while p1 gets slower, p2 is even slower than p1 (if that physical sense)?
According to Huygens principle the time taken is exactly the same. Each light ray arriving at a focus 'chooses' a path that takes exactly the same time. So the edge ray goes a further distance through fast air and a shorter distance through slow glass, the centre ray goes a short fast distance and a longer slow distance. But for them to come to the same focus the times must be the same. Huygens principle is one of the really clever bits of physics - it hints at relativity and quantum theory from 200 years before Einstein.