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Question #43585

Difficulty: 8/10 | 🟢 Free

The Question

A point source $S$ and a detector $D$ are placed in a large block of transparent dielectric material of refractive index $n = \sqrt{2}$ . They are located at a depth $h$ below the flat horizontal interface between the dielectric and air ( $n_{\text{air}} = 1$ ). The horizontal distance between $S$ and $D$ is $x = 2\sqrt{3}h$ . The source emits s-polarized electromagnetic waves (electric field perpendicular to the plane of incidence) of wavelength $\lambda$ in the dielectric. The detector records the interference between the direct wave from $S$ and the wave totally internally reflected from the interface. What is the minimum depth $h$ for which the detector records a local maximum in intensity?

Options

A.
$\frac{(2 + \sqrt{3})\lambda}{8}$
B.
$\frac{(2 + \sqrt{3})\lambda}{4}$
C.
$\frac{(2 + \sqrt{3})\lambda}{2}$
D.
$\frac{3(2 + \sqrt{3})\lambda}{8}$

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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

Diffraction vs Interference|Standing Wave Nodes/Antinodes|Boundary Condition Reflection|Binomial Approximation

Why This Question Is Tricky

Common Mistakes

This question tests the student's understanding of boundary conditions and phase shifts during Total Internal Reflection (TIR) in the near-field.

A common trap is mechanically assuming a standard $\pi$ phase shift (hard boundary) or $0$ phase shift (soft boundary) upon reflection.

However, for TIR, the phase shift is spatially dependent on the angle of incidence, which in this near-field geometry is determined by the source depth and separation.

Furthermore, students must correctly apply the Fresnel equations to find that the s-polarized wave undergoes a specific phase delay (here, $\pi/2$ ), not an advance, due to the evanescent wave penetration.

Misapplying the phase shift magnitude or sign leads directly to the trap options.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Wave Optics - Class 12
Concept	Diffraction vs Interference
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free