MHT CET · Physics · Ray Optics

The prism has refracting angle ' \(\mathrm{A}\) '. The second refracting surface of the prism is silvered. Light ray falling on first refracting surface with angle of incidence ' \(2 \mathrm{~A}\) ', reaches the second surface and returns back through the same path due to reflection at the silvered surface. The refractive index of the material of the prism is

A \(\frac{1}{2} \sin \mathrm{A}\)
B \(\frac{1}{2} \cos \mathrm{A}\)
C \(2 \sin A\)
D \(2 \cos A\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(2 \cos A\)

Step-by-step Solution

Detailed explanation

Normal incidence at silvered surface

\(\therefore \quad \mu=\frac{\sin \mathrm{i}}{\sin \mathrm{r}}=\frac{\sin 2 \mathrm{~A}}{\sin \mathrm{A}}=\frac{2 \sin \mathrm{A} \cos \mathrm{A}}{\sin \mathrm{A}}=2 \cos \mathrm{A}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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