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GATE 2024 PH – Question 12

Electromagnetic theory · reflection and transmission at normal and oblique incidences · 1 mark · Multiple choice

An unpolarized plane wave in dielectric medium 1 of index $n_1$ strikes medium 2 of index $n_2>n_1$ at angle $\tan^{-1}(n_2/n_1)$. Which statement is true?

  1. The reflected wave is unpolarized
  2. The reflected wave is polarized parallel to the plane of incidence
  3. The reflected wave is polarized perpendicular to the plane of incidence
  4. There is no transmitted wave

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Show answer and explanation

Correct answer: (C) The reflected wave is polarized perpendicular to the plane of incidence

Explanation

The angle of incidence $\theta_B=\tan^{-1}(n_2/n_1)$ is **Brewster's angle**.

At Brewster's angle:
- the reflected and refracted rays are at $90^\circ$ to each other;
- the reflection coefficient for light polarised **in the plane of incidence** (p-polarised, the "parallel" component) is zero.

So the reflected beam contains only the component polarised **perpendicular to the plane of incidence** (s-polarised). The reflected light is therefore plane polarised, perpendicular to the plane of incidence (option C). It is not unpolarised, and there is a transmitted wave in all cases.