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Question #42821

Difficulty: 8/10 | 🟢 Free

The Question

In a Young's Double Slit Experiment (YDSE), a white light source emitting wavelengths from $\lambda_V = 400 \text{ nm}$ to $\lambda_R = 700 \text{ nm}$ is used. The slit separation is $d = 1.0 \text{ mm}$ and the screen is at a distance $D = 1.0 \text{ m}$ from the slits. A transparent dielectric slab of thickness $t = 10 \text{ \mu m}$ is placed directly in front of the upper slit. The refractive index of the slab varies with wavelength $\lambda$ due to dispersion, having values $n_V = 1.52$ for violet light and $n_R = 1.50$ for red light. Determine the spatial spread $\Delta y$ of the zero-order maxima on the screen for the visible spectrum, and identify which color's zero-order maximum is closest to the geometric center of the screen.

Options

A.
$0.2 \text{ mm}$ , Red
B.
$0.2 \text{ mm}$ , Violet
C.
$0.0 \text{ mm}$ , White (All coincident)
D.
$5.1 \text{ mm}$ , White (All coincident)

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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

Dielectric Constant (K) Shift|Medium Dependency|Fringe Width Invariance

Why This Question Is Tricky

Common Mistakes

This question targets the misconception that inserting a dielectric slab in a YDSE setup with white light simply shifts the entire interference pattern uniformly, preserving a single white central maximum.

Students often blindly apply the formula $\Delta y = \frac{D}{d}(n-1)t$ assuming $n$ is a constant average value.

However, due to chromatic dispersion, the refractive index $n(\lambda)$ depends on the wavelength.

Consequently, the zero-order maximum (where the optical path difference is exactly zero) shifts by different amounts for different wavelengths, causing the central fringe to blur into a spectrum (chromatic aberration).

Furthermore, it tests the understanding of normal dispersion ( $n_V > n_R$ ), requiring the student to correctly deduce that the red maximum shifts less and thus remains closer to the geometric center.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electric Charges and Fields - Class 12
Concept	Dielectric Constant (K) Shift
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free