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Question #42008

Difficulty: 8/10 | 🟢 Free

The Question

In a Young's Double Slit Experiment, the slit separation is $d = 1.0 \text{ mm}$ and the screen distance is $D = 1.0 \text{ m}$ . A traveling microscope is used to measure the position of the central maximum on the screen. The maximum uncertainty in any single position reading is equal to the microscope's least count, $LC = 10 \text{ \mu m}$ . Initially, a hollow tube of length $L = 10.0 \text{ cm}$ containing vacuum is placed in front of one slit, and the position of the central maximum is recorded. A gas is then slowly pumped into the tube, and the position is recorded again. If the two recorded readings are exactly identical, what is the maximum possible value of $(\mu - 1)$ for the gas, where $\mu$ is its refractive index?

Options

A.
$2.0 \times 10^{-7}$
B.
$1.0 \times 10^{-7}$
C.
$5.0 \times 10^{-8}$
D.
$4.0 \times 10^{-7}$

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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

Least Count and Resolution Limits|Central Fringe Shift

Why This Question Is Tricky

Common Mistakes

This question tests the interplay between wave optics and instrumental error analysis.

A common trap is assuming that an unobservable shift implies the maximum physical shift is exactly one least count (LC).

However, because a shift measurement requires two independent readings (initial and final), each with an uncertainty bound of \pm LC, an identical before-and-after reading implies the true physical shift could be up to 2LC.

Students who fail to treat the measurement as a range will incorrectly calculate the maximum refractive index change using \Delta y = LC instead of 2LC, leading to a classic off-by-a-factor-of-two error.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Units and Measurements - Class 11 Part 1
Concept	Least Count and Resolution Limits
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free