Question

Two photons are moving in opposite direction with velocity c. Their relative velocity will be-
1. 2c
2. c
3. 0
4. \(\sqrt {2c} \)

Answer 1

Correct Answer - Option 2 : c

Concept:

Photon:

• A photon is a particle of light defined as a discrete bundle of electromagnetic energy. 
• The rest mass of the photon is zero.
• Photons are stable particles.
• They do not have any electric charge.
• Photons are not affected by the magnetic field and electric field.

Postulates of Special Relativity:

• The relativity postulate: the laws of physics apply in every inertial reference frame.
  The speed of light postulate: The speed of light in a vacuum is the same for any inertial reference frame (c = 3 x 10⁸ m/s).
• This is true no matter how fast a light source is moving relative to an observer.
• This is due to either light is an exception, or the classical velocity addition formula only works at low velocities.

Relativistic Velocity Addition:

If two photons moving with speed u and v relative to each other, then, relative velocity will be

\(V_R = \frac{u - v}{1-\frac{u\times v}{c^2}} \)

Calculation:

Given, photons are moving with speed c towards each other, therefore

u = c and v = - c

Using the relation of relative velocity

\(V_R = \frac{u - v}{1-\frac{u\times v}{c^2}} \)

\(⇒ V_R = \frac{c + c}{1+\frac{c\times c}{c^2}} \)

⇒ V_R = c

Hence, the relative velocity of photons will be c.