Optics 4 Question 23
24. A ray of light is incident at an angle of $60^{\circ}$ on one face of a prism which has an angle of $30^{\circ}$. The ray emerging out of the prism makes an angle of $30^{\circ}$ with the incident ray. Show that the emergent ray is perpendicular to the face through which it emerges and calculate the refractive index of the material of the lens.
(1978)
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Solution:
- Given $i _1=60^{\circ}, A=30^{\circ}, \delta=30^{\circ}$
From the relation
$$ \begin{array}{ll} & \delta=\left(i _1+i _2\right)-A \\ \text { we have, } & i _2=0^{\circ} \end{array} $$
i.e. the ray is perpendicular to the face from which it emerges.
$$ \begin{array}{rlrl} \text { Further, } & i _2 & =0^{\circ} \\ \therefore & & r _2 & =0^{\circ} \\ r _1+r _2 & =A \\ r _1 & =A=30^{\circ} \\ \mu=\frac{\sin i _1}{\sin r _1} & =\frac{\sin 60^{\circ}}{\sin 30^{\circ}}=\sqrt{3} \end{array} $$
