How do you measure the frequency of light?

Answer 1

Refractive index changes the velocity, frequency stays the same so wavelength must change. You can measure the change in speed directly with a clock. (In practice there is a slight extra complication that the refractive index of most real materials also varies with wavelength)

The bending is caused only by change in speed - it's called Fermat's principle and it's one of the cleverest things in physics.

What it says is that the light takes the path through the two materials that minimizes the total time to get from A-B.

You can even picture it in the 'real' world.

Suppose you had to rescue somebody in the ocean further down a beach.

You could jump in and swim directly to them, BUT you can run faster than you can swim, so it makes sense to run along the beach and then at some point get into the water and swim diagonally out toward them.

The ratio of how far you run and how far you swim - and so the point you enter the water - and therefore the angle between your running path and swimming path - only depends on the ratio of how fast you swim and how fast you run.

You pick them to minimize the time to the swimmer - just as the photon does.

How the photon 'knows' which path to take is the basis of quantum mechanics.