Question: 9. Find the value of the angle of emergence from the prism. Refractive index of the glass is \sqrt{3}.
(1) 60^{\circ}
(2) 30^{\circ}
(3) 45^{\circ}
(4) 90^{\circ}
Answer: Option (1)
Explanation:
From the given figure, the prism is a right-angled prism with one angle equal to 60^{\circ}.
The ray is incident normally on the first face, as indicated by the right-angle mark.
Since the angle of incidence at the first surface is 0^{\circ},
the ray enters the prism without deviation.
The ray then strikes the second face inside the prism.
The angle between the first and second faces is 60^{\circ},
hence the angle of incidence at the second face is 60^{\circ}.
For glass–air interface, the critical angle C is given by
\sin C = \frac{1}{\mu}.
Here, \mu = \sqrt{3}.
\sin C = \frac{1}{\sqrt{3}}.
C = 35.26^{\circ} approximately.
Since the angle of incidence 60^{\circ} is greater than the critical angle,
total internal reflection occurs at this face.
After reflection, the ray strikes the third face of the prism normally.
Hence, the angle of incidence at the emergent face is 0^{\circ},
so the ray emerges without deviation.
Therefore, the angle of emergence is equal to the angle the emergent face makes with the base,
which is 60^{\circ}.
Thus, the correct answer is 60^{\circ}.