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A ray of light is incident at $60 º$ on one face of a prism of angle $30 º$ and the emergent ray makes $30 º$ with the incident ray. The refractive index of the prism is:

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1.732

1.414

1.5

1.33

answer is A.

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Detailed Solution

For a prism

$i_{1} + i_{2} = A + δ$

Therefore, angle of emergence is

$i_{2} = A + δ - i_{1} = 30 + 30 - 60 = 0$

Also

$\begin{array}{l} r_{1} + r_{2} = A \\ i_{2} = O, r_{2} = O \\ r_{1} = A = 30^{\circ} \end{array}$

using Snell's law

$n = \frac{{sini}_{1}}{{sinr}_{1}} = \frac{\sin 60}{\sin 30} = 1.732$

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