Question

A ray of light is incident normally on one refracting surface of an equilateral prism. If the refractive index of the material of the prism is $1.5,$ then

• A. the emergent ray is deviated by $30^{\circ }$
• B. the emergent ray is deviated by $60^{\circ }$
• C. the emergent ray just graces the second reflecting surface
• D. the ray undergoes total internal reflection at second refracting surface
• E. the ray emerges normally from the second refracting surface

Answer 1

Answer: (B)

The ratio of sine of the angle of incidence to sine of angle of refraction $(r)$ is a constant called refractive index.
i.e. $\frac{\sin i}{\sin r}=\mu$ (a constant). For two media, Snell's law can be written as,
${}_1{\mu }_2=\frac{{\mu }_2}{{\mu }_1}=\frac{\sin i}{\sin r}$
Given, refractive index of a prism
$n=1.5=\frac{3}{2}$
As,$\mu =\frac{1}{\sin \theta }\Rightarrow \mu =\frac{1}{\sin 60^{\circ }}$
$\mu =\frac{2}{\sqrt{3}}\Rightarrow \sin C=\frac{1}{n}$
$\sin C=\frac{2}{3}\Rightarrow C={\sin }^{-1}\frac{2}{3}$
$C=42^{\circ }$
Angle of incidence $>$ critical angle
So, total internal reflection takes places at second refracting surface.