MHT CET · Physics · Wave Optics
The angle of prism is A and one of its refracting surface is silvered. Light rays falling at an angle of incidence ' \(2 \mathrm{~A}\) ' on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index of the material of the prism is
- A \(2 \sin \left(\frac{A}{2}\right)\)
- B \(2\ tan\ A\)
- C \(2\ cos\ A\)
- D \(2\ sin\ A\)
Answer & Solution
Correct Answer
(C) \(2\ cos\ A\)
Step-by-step Solution
Detailed explanation
Given: Angle of Prism \(=\mathrm{A}, \mathrm{I}=2 \mathrm{~A}\)
As DE is falling normally on the silvered side \(\mathrm{AC}\),
\(\begin{aligned}
& \mathrm{r}=90-(90-\mathrm{A}) \\
& \mathrm{r}=\mathrm{A}
\end{aligned}\)
Using Snell's law,
\(\frac{\sin \mathrm{i}}{\sin \mathrm{r}}=\frac{\sin 2 \mathrm{~A}}{\sin \mathrm{A}}=\frac{2 \sin \mathrm{A} \cos \mathrm{A}}{\sin \mathrm{A}}=2 \cos \mathrm{A}\)
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