Question

A ray of light passes through four transparent media with refractive indices \(\mu _{1}\), \(\mu _{2}\), \(\mu _{3}\) and \(\mu _{4}\) as shown in the figure. The surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, then

• A. \(\mu _{1}=\mu _{2}\)
• B. \(\mu _{2}=\mu _{3}\)
• C. \(\mu _{3}=\mu _{4}\)
• D. \(\mu _{4}=\mu _{1}\)

Hint:

With parallel boundaries, the product of refractive index and sine of the angle stays constant across all the media.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
All boundaries are parallel, so Snell's law at successive faces gives \(\mu_{1}\sin\theta_{1}=\mu_{2}\sin\theta_{2}=\mu_{3}\sin\theta_{3}=\mu_{4}\sin\theta_{4}\).

Step 2: Parallel rays
AB is in the first medium and CD is in the fourth. CD parallel to AB means \(\theta_{4}=\theta_{1}\).

Step 3: Result
Then \(\mu_{1}\sin\theta_{1}=\mu_{4}\sin\theta_{1}\), so \(\mu_{4}=\mu_{1}\). The middle media can have any indices.

Final Answer:
The emergent ray is parallel to the incident ray when \(\mu_{4}=\mu_{1}\). \[ \boxed{\text{(D) }\mu_{4}=\mu_{1}} \]