JEE Mains · Physics · STD 12 - 9. Ray optics and optical instruments
The refractive index of a prism with apex angle \(A\) is \(\cot A / 2\). The angle of minimum deviation is _______.
- A \(\delta_{\mathrm{m}}=180^{\circ}-\mathrm{A}\)
- B \(\delta_m=180^{\circ}-3 \mathrm{~A}\)
- C \(\delta_m=180^{\circ}-4 \mathrm{~A}\)
- D \(\delta_{\mathrm{m}}=180^{\circ}-2 \mathrm{~A}\)
Answer & Solution
Correct Answer
(D) \(\delta_{\mathrm{m}}=180^{\circ}-2 \mathrm{~A}\)
Step-by-step Solution
Detailed explanation
\(\mu=\frac{\sin \left(\frac{A+\delta m}{2}\right)}{\sin \frac{A}{2}}\) \(\frac{\cos \frac{A}{2}}{\sin \frac{A}{2}}=\frac{\sin \left(\frac{A+\delta m}{2}\right)}{\sin \frac{A}{2}}\) \(\sin \left(\frac{\pi}{2}-\frac{A}{2}\right)=\sin \left(\frac{A+\delta_m}{2}\right)\)…
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