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A ray of light is incident at an angle of $60^{0}$ on one face of a prism which has refracting angle of $30^{0}$ .The ray emerging out of the prism makes an angle of $30^{0}$ with the incident ray. If the refractive index of the material of the prism is $μ = \sqrt{a}$ , find the value of $a$ .

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answer is 3.

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Detailed Solution

Given $i = 60^{0}, δ = 30^{0} & A = 30^{0}$
We have $δ = i + e - A$ …….(1)
From Eq. (i), we get
$30^{0} = 60^{0} + e - 30^{0} (o r) e = 0$
So $r_{2}$ is also zero, then $r_{1} = A = 30^{0}$

So, $μ = \frac{\sin i}{\sin r_{1}} = \frac{\sin 60^{0}}{\sin 30^{0}} = \sqrt{3}$

Hence the value of $a = 3$

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