An unpolarized plane electromagnetic wave in a dielectric medium 1 is incident on
a plane interface that separates medium 1 from another dielectric medium 2.
Medium 1 and medium 2 have refractive indices n1 and n2, respectively, with
n2 > n1. If the angle of incidence is tan-1 (
n2
n1
), which one of the following
statements is true?
Options:
(A) The reflected wave is unpolarized
(B) The reflected wave is polarized parallel to the plane of incidence
(C) The reflected wave is polarized perpendicular to the plane of incidence
(D) There is no transmitted wave
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2024 Q.12)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Electromagnetic Theory** within *Section 3: Electromagnetic Theory* (1 Mark, 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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