Question

A ray of light is incident on a glass sphere of refractive index $3/2$. What should be the angle of incidence so that the ray which enters the sphere does not come out of the sphere?

• A. $ta{n}^{-1}\left(2/3\right)$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

Answer: (C)

${90}^{\circ }$

For the light to not come out of the sphere, $e$ must be greater than or equal to ${90}^{\circ }$.

From Snell's law,

$\mu \sin r=\sin e$

Also at point D,

$\mu \sin r=\sin i$

Hence, $\sin i=\sin e$

Since $e$ is greater than or equal to ${90}^{\circ }$, i has to be greater than or equal to ${90}^{\circ }$.

But more than ${90}^{\circ }$ means that the ray is not incident on the sphere. Therefore the only incident angle possible is ${90}^{\circ }$