First slide

Ray optics

Question

The refracting angle of a prism is A, and refractive index of the material of the prism is cot (A / 2). The angle of minimum deviation is

Moderate

A

90° - A
B

180° + 2A
C

180° - 3A
D

180° - 2A

Solution

$As μ = \frac{\sin (\frac{A + δ}{2})}{\sin (\frac{A}{2})}$
$\cot \frac{A}{2} = \frac{\sin (\frac{A + δ}{2})}{\sin (\frac{A}{2})} [∵ μ = \cot \frac{A}{2}]$
$\frac{\cos (\frac{A}{2})}{\sin (\frac{A}{2})} = \frac{\sin (\frac{A + δ}{2})}{\sin (\frac{A}{2})}$
$\begin{array}{l} \sin (\frac{π}{2} - \frac{A}{2}) = \sin (\frac{A}{2} + \frac{δ}{2}); \frac{π}{2} - \frac{A}{2} = \frac{A}{2} + \frac{δ}{2} \\ ∴ δ = π - 2 A = 180 ° - 2 A \end{array}$

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