Question

A ray is incident at an angle of incidence $i$ on one surface of a small angled prism (with angle of prism $8^{\circ })$ and emerges normally from the opposite surface. If the refractive index of the material of prism is $\frac{3}{2},$ then the angle of incidence is nearly equal to

• A. ${12}^{\circ }$
• B. $8^{\circ }$
• C. ${14}^{\circ }$
• D. $6^{\circ }$

Answer 1

The correct option is A ${12}^{\circ }$



By Snell's law at point P,

$\frac{\sin i}{\sin r_1}=\mu$

For small value of $\theta$,

$\sin \theta \approx \theta$

$\frac{\sin i}{\sin r_1}=\frac{i}{r_1}$

$\frac{i}{r_1}=\mu$

$r_1+r_2=A$

$r_2=0$

$r_1=A$

$i=\mu A$

On putting the value of $\mu$ and $A$

$i=\frac{3}{2}\times 8^{\circ }$

$={12}^{\circ }$