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Question #43596

Difficulty: 8/10 | 🟢 Free

The Question

In an optics experiment, a student determines the refractive index $\mu$ of a transparent medium by measuring the polarizing angle (Brewster's angle) $i_p$ for unpolarized light incident from air. The measured value of the polarizing angle is $i_p = 60^\circ$ . If the spectrometer used has a least count of $\Delta i_p = 0.1^\circ$ , what is the maximum percentage error in the calculated value of the refractive index?

Options

A.
$\frac{2\pi}{9\sqrt{3}} \%$
B.
$\frac{40}{\sqrt{3}} \%$
C.
$\frac{2\pi}{9} \%$
D.
$\frac{1}{6} \%$

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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|Relative Error Propagation in Powers

Why This Question Is Tricky

Common Mistakes

This question tests the propagation of errors through trigonometric functions, specifically targeting the common oversight of unit dimensions in differential calculus.

Students frequently apply the differential $d(\tan \theta) = \sec^2 \theta \, d\theta$ and substitute $d\theta$ directly in degrees, leading to a massive overestimation of the error (Option B).

The mathematical framework of calculus assumes angles are dimensionless ratios (radians); thus, any angular uncertainty must be converted to radians before evaluating the differential error.

Additionally, it distinguishes between absolute error and relative percentage error, trapping students who calculate the absolute error $d\mu$ and forget to divide by the original refractive index $\mu$ (Option C), or those who incorrectly apply a linear small-angle approximation $\Delta \mu / \mu = \Delta i_p / i_p$ (Option D).

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