# What is the Speed of a Photon with Respect to Another Photon If (A) the Two Photons Are Going in the Same Direction and (B) They Are Going in Opposite Directions? - Physics

Short Note

What is the speed of a photon with respect to another photon if (a) the two photons are going in the same direction and (b) they are going in opposite directions?

#### Solution

(a) In relativity, the relative speed of two objects (v_(rel)) moving in the same direction with speeds u and v is given by v_(rel) = (u - v)/(1-(uv)/c^2) ...(1)

As the photons are moving with the speed of light, u = c and v = c.
On substituting the values of u and v in equation (1), we get :

v_(rel) = 0

Thus, relative velocity of a photon with respect to another photon will be 0, when they are going in the same direction.
(b) In relativity, relative speed of two objects moving in opposite directions with speeds u and v is given by

v_(rel) = (u+v)/(1+(uv)/c^2)     ....(2)

We know that a photon travels with the speed of light. Therefore, u = c and v = c
On substituting the values of u and v in equation (2), we get :

v_(rel) = c

Thus, the relative velocity of a photon with respect to another photon will be equal to the speed of light when they are going in opposite directions.

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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 20 Photoelectric Effect and Wave-Particle Duality
Short Answers | Q 3 | Page 363