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Question

A ray of light passing through a prism having $μ = 2$ suffer minimum deviation. It is found that angle of incidence is double the angle of refraction within the prism. Find angle of the prism.

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Solution

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if $∠ i =$ incidence angle
$∠ r =$ refracted angle

$∠ i = 2 \times ∠ r$

$\frac{sin i}{sin r} = μ$

$\frac{sin 2 r}{sin r} = \frac{2 sin r cos r}{sin r} = 2 cos r = 2$

$cos r = \frac{1}{2}$

$r = 4 5^{\circ}$

For minimum deviation, $r_{1} = r_{2} = r$

$∴ a = 2 \times r$

$∠ a = 2 \times 4 5^{\circ}$

$= 9 0^{\circ}$

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