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GATE 2025 PH – Question 16

Optical Physics · Wave equation: plane and spherical waves, superposition of waves, standing waves, phase and group velocities · 1 mark · Multiple choice

Which one of the following is correct for phase velocity $v_p$ and group velocity $v_g$? ($c$ is the speed of light in vacuum)

  1. For relativistic matter waves, $v_pv_g>c^2$
  2. For electromagnetic waves in a medium, $v_p$ represents the speed with which energy propagates
  3. For electromagnetic waves in a medium, both $v_p$ and $v_g$ can be more than $c$
  4. For matter waves in free space, $v_p\ne v_g$

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Correct answer: (D) For matter waves in free space, $v_p\ne v_g$

Explanation

For free nonrelativistic matter waves $v_p=v/2$ and $v_g=v$. Relativistically $v_pv_g=c^2$, rather than exceeding it. Group velocity is the usual energy-transport velocity in a transparent dispersive medium.

Official GATE 2025 answer key: https://gate2026.iitg.ac.in/doc/download/2025_Key/PH_Keys.pdf