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Question #43595

Difficulty: 8/10 | 🟢 Free

The Question

An unpolarized light beam of time-varying intensity $I(t) = I_0 \cos^2(\omega t)$ and wavelength $\lambda$ is incident from vacuum onto a flat glass slab of refractive index $n = \sqrt{3}$ . The angle of incidence is exactly the Brewster's angle. The transmitted beam, having a cross-sectional area $A$ normal to its direction of propagation, immediately passes through a polarizing filter. The transmission axis of the filter rotates with time as $\phi(t) = \omega t$ , where $\phi=0$ corresponds to the plane of incidence. What is the time-averaged photon flux (number of photons per second) emerging from the polarizing filter? (Assume $h$ is Planck's constant and $c$ is the speed of light)

Options

A.
$\frac{15 I_0 A \lambda}{64 h c}$
B.
$\frac{7 I_0 A \lambda}{32 h c}$
C.
$\frac{3 I_0 A \lambda}{16 h c}$
D.
$\frac{13 I_0 A \lambda}{64 h c}$

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|Intensity and Photon Flux|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the understanding of partial polarization at dielectric interfaces and the superposition of incoherent orthogonal components through a time-varying transmission gate.

The primary trap lies in assuming that the transmitted light is either completely polarized (like the reflected beam) or unpolarized with a reduced total intensity.

If a student incorrectly treats the transmitted beam as unpolarized with intensity $\frac{7}{8}I_0\cos^2(\omega t)$ , they will apply a simple factor of $1/2$ for the polarizer, yielding $\frac{7}{32}I_0$ , missing the non-linear correlation between the incident intensity oscillation and the polarizer's rotation.

Correctly solving requires independently tracking the parallel and perpendicular components and integrating their respective Malus's Law projections over time.

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