KCET · Physics · Ray Optics
A ray of light passes through four transparent media with refractive index \( n_{1}, n_{2}, n_{3} \) and \( n_{4} \) as
shown. The surfaces of all media are parallel
If the emergent ray \( D E \) is parellel to incident ray \( A B \), then
- A \( n_{1}=n_{4} \)
- B \( n_{2}=n_{4} \)
- C \( n_{3}=n_{4} \)
- D \( n_{1}=\frac{n_{2}+n_{3}+n_{4}}{3} \)
Answer & Solution
Correct Answer
(A) \( n_{1}=n_{4} \)
Step-by-step Solution
Detailed explanation
Given, \( 4 \) transparent media \( n_{1}, n_{2}, n_{3} \) and \( n_{4} \) are parallel to each other and a ray of light passes through it.
Then by Snell's law for multiple media, we have
\[
n_{1} \sin \theta_{1}=n_{4} \sin \theta_{4}
\]
But \( \theta_{1}=\theta_{4} \)
Therefore, \( n_{1}=n_{4} \)
Then by Snell's law for multiple media, we have
\[
n_{1} \sin \theta_{1}=n_{4} \sin \theta_{4}
\]
But \( \theta_{1}=\theta_{4} \)
Therefore, \( n_{1}=n_{4} \)
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