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Question #43218

Difficulty: 8/10 | 🟢 Free

The Question

A beam of unpolarized white light is incident from a transparent liquid of refractive index $n_1 = \sqrt{2}$ onto a flat glass slab. The angle of incidence is $\theta_i = 60^\circ$ . The refractive index of the glass varies with the wavelength $\lambda$ of light according to the Cauchy-type relation $n_2(\lambda) = \sqrt{2 + \frac{A}{\lambda^2}}$ , where $A$ is a positive constant. The reflected beam is passed through a polarizing filter. It is observed that for a specific spectral component of wavelength $\lambda_0$ , the reflected light is completely blocked when the transmission axis of the polarizer is oriented parallel to the plane of incidence. Calculate the angular dispersion (the angle between the refracted rays) inside the glass slab between the spectral components of wavelength $\lambda_0$ and $\lambda' = 2\lambda_0$ .

Options

A.
$15^\circ$
B.
$30^\circ$
C.
$45^\circ$
D.
$0^\circ$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Dispersion vs Deviation (703)|Brewster's Law (725)|Vector Decomposition Ambiguity (396)

Why This Question Is Tricky

Common Mistakes

This question tests the student's understanding of frequency-dependent polarization and dispersion.

The primary trap is the 'monochromatic bias', where students incorrectly assume that if a polychromatic beam is incident at Brewster's angle, the entire reflected beam is perfectly polarized and all refracted rays satisfy the $\theta_i + \theta_r = 90^\circ$ condition (leading to the trap answer of $0^\circ$ ).

By coupling Brewster's Law with a Cauchy-type dispersion relation, the problem forces students to recognize that Brewster's angle is strictly wavelength-dependent.

Furthermore, it tests the correct application of Brewster's formula for a relative interface ( $\tan \theta_B = n_2/n_1$ ) rather than the absolute formula ( $\tan \theta_B = n$ ), and verifies their understanding of polarizer transmission axes relative to the plane of incidence.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Ray Optics and Optical Instruments - Class 12
Concept	Dispersion vs Deviation
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free