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: (D)

Key Concept: The ratio of sine of the angle of incidence to sine of angle of refraction $\left(r\right)$ 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.