JEE Mains · Physics · STD 12 - 9. Ray optics and optical instruments
If the refractive index of the material of a prism is \(\cot \left(\frac{A}{2}\right)\), where \(A\) is the angle of prism then the angle of minimum deviation will be
- A \(\pi-2 \mathrm{~A}\)
- B \(\frac{\pi}{2}-2 \mathrm{~A}\)
- C \(\pi-\mathrm{A}\)
- D \(\frac{\pi}{2}-\mathrm{A}\)
Answer & Solution
Correct Answer
(A) \(\pi-2 \mathrm{~A}\)
Step-by-step Solution
Detailed explanation
\( \cot \frac{A}{2}=\frac{\sin \left(\frac{A+\delta_{\min }}{2}\right)}{\sin \frac{A}{2}} \) \( \Rightarrow \cos \frac{A}{2}=\sin \left(\frac{A+\delta_{\min }}{2}\right) \) \( \frac{A+\delta_{\min }}{2}=\frac{\pi}{2}-\frac{A}{2} \) \( \delta_{\min }=\pi-2 A\)
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