Before You Begin

Question #43195

Difficulty: 8/10 | 🟢 Free

The Question

A plane electromagnetic wave traveling in vacuum ( $n_1 = 1$ ) is incident on a flat dielectric medium of refractive index $n_2 = \sqrt{3}$ occupying the half-space $z \le 0$ . The incident wave vector is $\vec{k}_i = \frac{\omega}{c} \left( \frac{\sqrt{3}}{2}\hat{i} - \frac{1}{2}\hat{k} \right)$ . The electric field amplitude vector of the incident wave is $\vec{E}_i = E_0 (\hat{i} + 2\hat{j} + \sqrt{3}\hat{k}) \text{ V/m}$ , where $E_0$ is a real constant. Which of the following represents the electric field amplitude vector $\vec{E}_r$ of the reflected wave?

Options

A.
$-E_0 \hat{j} \text{ V/m}$
B.
$E_0 \hat{j} \text{ V/m}$
C.
$-\frac{1}{2} E_0 (\hat{i} + 2\hat{j} + \sqrt{3}\hat{k}) \text{ V/m}$
D.
$\frac{1}{2} E_0 (\hat{i} - \sqrt{3}\hat{k}) \text{ V/m}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Snell’s Law Vector Form|Brewster's Law|Vector Projection

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to transition from scalar optics to vector field analysis at an interface.

The primary trap lies in failing to recognize that the incident wave is at the Brewster angle, which dictates that the p-polarized (TM mode) component of the electric field completely vanishes upon reflection.

Students who blindly apply a scalar reflection coefficient to the entire vector $\vec{E}_i$ will incorrectly scale all components, leading to option C.

Furthermore, students must correctly identify the plane of incidence to separate the s- and p-polarized components; using 2D geometry without vector projection leads to incorrect field orientations.

The negative sign in the Fresnel coefficient $r_s$ also traps students who ignore the phase shift upon reflection from a higher index medium.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Ray Optics and Optical Instruments - Class 12
Concept	Snell’s Law Vector Form
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free