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Question #43197

Difficulty: 8/10 | 🟢 Free

The Question

A plane electromagnetic wave of vacuum wavelength $\lambda_0$ is propagating inside a non-magnetic dielectric block of refractive index $n = 2$ . The wave is incident on the flat interface between the dielectric and vacuum at an angle of incidence $\theta = 60^\circ$ . The electric field vector is polarized perpendicular to the plane of incidence. Due to total internal reflection, a standing wave pattern is formed along the direction normal to the interface. What is the perpendicular distance from the interface to the first antinode of the electric field inside the dielectric?

Options

A.
$\frac{\lambda_0}{2\pi} \tan^{-1}(\sqrt{2})$
B.
$\frac{\lambda_0}{2\pi} \tan^{-1}(4\sqrt{2})$
C.
$\frac{\lambda_0}{4}$
D.
$\frac{\lambda_0}{8}$

Check Your Answer

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

Total Internal Reflection (TIR)|Standing Wave Nodes/Antinodes|Vector Cross-Products

Why This Question Is Tricky

Common Mistakes

This question tests the student's understanding of boundary conditions during Total Internal Reflection (TIR).

A common misconception is treating a TIR interface as a 'hard wall' (perfect conductor), which would incorrectly place a node exactly at the boundary and lead to an antinode at $\lambda_z/4$ (Option C) or $\lambda_n/4$ (Option D).

In reality, the boundary condition requires continuity of the electric field and its derivative, leading to an evanescent wave in the vacuum and a specific phase shift (related to the Goos-Hänchen effect) for the reflected wave.

By forcing the calculation of this phase shift for s-polarization and applying it to the standing wave superposition, the problem discriminates between geometric approximations and rigorous wave optics.

Option B serves as a lethal trap for students who incorrectly apply the p-polarization Fresnel phase shift formula.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Ray Optics and Optical Instruments - Class 12
Concept	Total Internal Reflection (TIR)
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free