A photon of energy hv and momentum hv/c collides with an electron at rest. After the collision, the scattered electron and the scattered photon each make an angle of with the initial direction of motion. The ratio of frequency of scattered and incident photon is :
This is an example of Compton Scattering, which is the scattering of a photon by an electron. It results in a decrease in the energy (thus a decrease in frequency) of the photon.
Let the frequency of scattered photons be
By conservation of momentum in the vertical direction, the momentum of scattered electrons and photons are the same and equal to
By conservation of linear momentum in the horizontal direction,