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Question #42697

Difficulty: 8/10 | 🟢 Free

The Question

A transparent, non-magnetic, non-polar dielectric slab of thickness $t = 2.4 \text{ \mu m}$ is placed directly in front of one of the slits in a Young's Double Slit Experiment (YDSE) setup. The experiment uses monochromatic light of wavelength $\lambda = 400 \text{ nm}$ . To determine the optical properties of the slab, it is tested in an electrostatic setup: when the slab completely fills the space between the plates of a parallel plate capacitor connected to a constant DC voltage source, the energy stored in the capacitor is $U_1 = 90 \text{ \mu J}$ . When the slab is removed, leaving air between the plates while still connected to the same voltage source, the stored energy becomes $U_2 = 10 \text{ \mu J}$ . Assuming the relative permittivity of the dielectric material is frequency-independent, by how many fringes does the central maximum shift on the screen due to the insertion of the slab?

Options

A.
12
B.
18
C.
4
D.
48

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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

Dielectric Slab Displacement|Central Fringe Shift|Refractive Index Relativity

Why This Question Is Tricky

Common Mistakes

This question tests the synthesis of electrostatics and physical optics via Maxwell's equations.

A common trap for students is to blindly substitute the electrostatic dielectric constant $K$ as the optical refractive index $n$ in the path difference formula $\Delta x = (n-1)t$ .

By doing so, they calculate a path difference based on $n=9$ instead of the correct $n=\sqrt{K}=3$ , leading directly to the trap answer of 48 fringes.

The problem enforces the understanding that optical refractive index is governed by the high-frequency limit of permittivity, where $n^2 \approx \epsilon_r$ for non-magnetic dielectrics.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electrostatic Potential and Capacitance - Class 12
Concept	Dielectric Slab Displacement
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free