A plane polarized electromagnetic wave propagating in y-z plane is incident at the
interface of two media at Brewster's angle. Taking z = 0 as the boundary
between the two media, the electric field of the reflected wave is given by
Eሬ⃗ோ = Aோ cos ቈk ቊ√3
2 y - 1
2 z ቋ - 𝜔t x ො
then which among the following statements are correct?
Options:
(A) The angle of refraction is
గ
(B) Ratio of permittivity of the medium of refraction (𝜖ଶ) with respect to the medium
on incidence (𝜖ଵ),
ఢమ
ఢభ
= 3
(C) The incident wave can have components of its electric field in y-z plane
(D) The angle of reflection is
గ
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2022 Q.58)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Electromagnetic Theory** within *Section 3: Electromagnetic Theory* (2 Marks, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Electromagnetic Theory:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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