A photon and electron collision

[feliciasutanto]

Homework Statement

Consider a photon colliding with an electron and scattered directly backward. If the electron is initially at rest and the incident photon has frequency f, determine the frequency of the back-scattered photon

Homework Equations

The Attempt at a Solution

Since the photon has no rest mass, then it should always move in speed of light. Therefore the frequency before and after the collision must be the same.

 

[vela]

So red light and blue light, both of which travel with speed $c$, have the same frequency and wavelength?