Before You Begin

Question #43204

Difficulty: 8/10 | 🟢 Free

The Question

In one arm of a Michelson interferometer, a parallel beam of light travels through air (refractive index $\mu_{\text{air}} = 1$ ). A transparent glass slab of thickness $t$ and refractive index $\mu = \frac{4}{3}$ is inserted into this arm. The slab is tilted such that the angle of incidence of the light beam on the slab is $53^\circ$ . Which of the following expressions correctly represents the additional optical path length introduced by the insertion of the slab? (Take $\sin 53^\circ = \frac{4}{5}$ )

Options

A.
$\frac{7}{15} t$
B.
$\frac{1}{3} t$
C.
$\frac{2}{3} t$
D.
$\frac{5}{12} t$

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

Lateral Shift in Slab|Phase Difference vs. Path Difference|Binomial Approximation

Why This Question Is Tricky

Common Mistakes

This question tests the student's understanding of optical path difference beyond the standard normal-incidence formula $\Delta x = (\mu - 1)t$ .

A common trap is blindly applying this formula (yielding $t/3$ ) or simply replacing the thickness $t$ with the slanted path $t/\cos r$ to get $(\mu - 1)t/\cos r$ (yielding $5t/12$ ).

Students fail to account for the lateral shift of the ray, which alters the geometric distance the light would have traveled in air to reach the same parallel wavefront.

The rigorous approach requires calculating the phase difference between the shifted and unshifted wavefronts, leading to the exact relation $\Delta x = t(\mu \cos r - \cos i)$ .

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Ray Optics and Optical Instruments - Class 12
Concept	Lateral Shift in Slab
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free