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

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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

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

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

⇒ VR = c

Hence, the relative velocity of photons will be c.

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