A ray incident on one face of a prism of angle \( 30^\circ \) and refractive index \( \sqrt{2} \) falls normally on the second face. What is the angle of incidence on the first face?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 45^\circ \)
Inside a prism the angles of refraction at the two faces add up to the angle of the prism, \( r_1+r_2=A \). A ray that falls normally on the second face has \( r_2=0 \), so all the bending happens at the first face, where Snell’s law applies.
The angle of refraction at the first face is:
\( \begin{aligned} r_1 &= A-r_2 \\ &= 30^\circ-0 \\ &= 30^\circ \end{aligned} \)
Snell’s law at the first face gives:
\( \begin{aligned} \sin i &= n\sin r_1 \\ &= \sqrt{2}\times\sin30^\circ \\ &= \frac{1}{\sqrt{2}} \end{aligned} \)
\( \Rightarrow\; i=45^\circ \)