Question

A light ray incident in a medium of refractive index $\frac{4}{3}$ is shown in diagram. Interface separating the two medium lies in $xy$ plane. Vector along incident ray is $3\hat{i}-4\hat{j}$. Then :

• A. Angle of incidence is ${37}^{\circ }$
• B. The angle of refraction is ${60}^{\circ }$
• C. The angle of refraction is ${30}^{\circ }$
• D. If angle of incidence of the incident ray is greater than the critical angle then total internal reflection takes place

Answer 1

The correct option is C The angle of refraction is ${30}^{\circ }$

incident ray

$\overrightarrow{r}=3\hat{i}-4\hat{j}$

$\tan i=\frac{3}{4}$

$\sin i=\frac{3}{5}$

use snell's law

${\mu }_1\times Sini={\mu }_2\times Sinr$

$\left(\sin i\right)\times \frac{4}{3}=\frac{8}{5}Sinr$

$\frac{3}{5}\times \frac{4}{3}=\frac{8}{5}\sin r$

$\sin r=\frac{1}{2}$

$r={30}^0$