A prism is made up of a material of refractive index $\sqrt{3}$ . The angle of the prism is $A^{0}$ . If the angle of minimum deviation is equal to the angle of the prism, then the value of A is :

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$30^{0}$

$60^{0}$

$45^{0}$

$75^{0}$

answer is C.

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Detailed Solution

Given. $μ = \sqrt{3}$ , $δ_{m} = A$

$μ = \frac{\sin (\frac{A + δ_{m}}{2})}{\sin \frac{A}{2}}$

or $\sqrt{3} = \frac{\sin (\frac{A + A}{2})}{\sin \frac{A}{2}} = \frac{\sin A}{\sin \frac{A}{2}} = \frac{2 \sin \frac{A}{2} \cos \frac{A}{2}}{\sin \frac{A}{2}} = 2 \cos \frac{A}{2}$

$∴$ $\cos \frac{A}{2} = \frac{\sqrt{3}}{2} = \cos 30^{0}$ or , $A = 60^{0}$

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