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Question #43743

Difficulty: 8/10 | 🟢 Free

The Question

An unpolarized light beam traveling in a vacuum (refractive index $n_1 = 1$ ) is incident on a flat dielectric surface (refractive index $n_2 = \sqrt{3}$ ) at the Brewster angle $\theta_B$ . Let $\langle \vec{S}_R \rangle$ and $\langle \vec{S}_T \rangle$ represent the time-averaged Poynting vectors of the reflected and transmitted beams, respectively. Calculate the ratio of their magnitudes, $\frac{|\langle \vec{S}_R \rangle|}{|\langle \vec{S}_T \rangle|}$ .

Options

A.
$\frac{\sqrt{3}}{7}$
B.
$\frac{1}{7}$
C.
$\frac{1}{8}$
D.
$\frac{3}{7}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Brewster's Law|Magnitude Ratio Identity|Vector Cross-Products

Why This Question Is Tricky

Common Mistakes

This question tests the misconception that the magnitude of the Poynting vector (intensity) is a conserved scalar quantity across a boundary ( $I_0 = I_R + I_T$ ).

Students who make this error will calculate $I_T = I_0 - I_0/8 = 7I_0/8$ , leading to the incorrect ratio of $1/7$ .

The correct physical principle requires applying conservation of energy to the normal component of the Poynting vector ( $\vec{S} \cdot \hat{n}$ ), which accounts for the change in the beam's cross-sectional area due to refraction ( $\cos \theta_i$ vs $\cos \theta_t$ ).

Furthermore, it tests the knowledge that at Brewster's angle, unpolarized light yields a purely s-polarized reflected beam, requiring the use of Fresnel equations rather than simple scalar assumptions.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Wave Optics - Class 12
Concept	Brewster's Law
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free