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Question #43138

Difficulty: 8/10 | 🟢 Free

The Question

A glass prism of refracting angle $A = 60^\circ$ and refractive index $\mu_p = \sqrt{3}$ is placed in air. An s-polarized monochromatic light beam (electric field perpendicular to the plane of incidence) of vacuum wavelength $\lambda$ is incident on the first face of the prism at the angle of minimum deviation. The second (exit) face of the prism is coated with a uniform transparent thin film of refractive index $\mu_c = 1.5$ and thickness $t$ . What is the minimum non-zero thickness $t$ of the film such that the intensity of the light reflected back into the prism from the exit face is maximized?

Options

A.
$\frac{\lambda}{\sqrt{6}}$
B.
$\frac{\lambda}{2\sqrt{6}}$
C.
$\frac{\lambda}{3}$
D.
$\frac{2\lambda}{3\sqrt{3}}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Prism Minimum Deviation|Boundary Condition Reflection|Wave Equation Sign Convention

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to bridge geometric ray optics and wave optics while rigorously evaluating boundary conditions for phase shifts.

The primary trap lies in the misapplication of Stokes' relations.

Students often blindly assume thin-film interference involves a $\pi$ phase shift, leading them to incorrectly use the destructive interference condition ( $2\mu t \cos r = \lambda/2$ ) for a reflection maximum.

Here, both reflections occur at boundaries transitioning from a higher to a lower refractive index ( $\sqrt{3} \to 1.5$ and $1.5 \to 1$ ), meaning neither reflected ray undergoes a $\pi$ phase shift.

Furthermore, specifying s-polarization prevents ambiguity, as the second reflection occurs beyond the Brewster angle.

Students may also fail to calculate the correct refracted angle inside the film, erroneously using the prism's internal angle of incidence ( $30^\circ$ ) or assuming normal incidence.

Quick Facts About This Question

Question Information

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