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Question #43741

Difficulty: 8/10 | 🟢 Free

The Question

A narrow beam of unpolarized monochromatic light is incident on the first face of a transparent glass prism having a refracting angle $A$ and refractive index $n$ . It is observed that the light reflected from the first face is completely plane-polarized. Simultaneously, the light transmitted through the prism undergoes minimum deviation, with the angle of minimum deviation being $\delta_m$ . Which of the following expressions correctly represents the refractive index $n$ of the prism in terms of $\delta_m$ ?

Options

A.
$\cot\left(\frac{\pi - \delta_m}{4}\right)$
B.
$\tan\left(\frac{\pi - \delta_m}{4}\right)$
C.
$\cot\left(\frac{\pi + \delta_m}{4}\right)$
D.
$\tan\left(\frac{\pi + \delta_m}{4}\right)$

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|Prism Minimum Deviation|Small Angle Approximation

Why This Question Is Tricky

Common Mistakes

This question tests the synthesis of Brewster's Law and the condition for minimum deviation in a prism.

A common trap is attempting to blindly solve the standard minimum deviation formula $n = \sin((A+\delta_m)/2) / \sin(A/2)$ alongside $\tan i_B = n$ without recognizing the geometric constraint forced by the coupling of these two phenomena.

By applying Snell's law at the Brewster angle, students must derive the rigid constraint $i_B + r_1 = \pi/2$ .

Failing to identify this relationship leads to an over-constrained system of trigonometric equations that is difficult to resolve, highlighting the importance of analyzing the physical geometry over mere algebraic manipulation.

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