Question

A ray of laser of a wavelength $630\text{nm}$ is incident at an angle of ${30}^{\circ }$ at the diamond-air interface. It is going from diamond to air. The refractive index of diamond is $2.42$ and that of air is $1.$ Choose the correct option.

• A. refraction is not possible
• B. angle of refraction is ${53.4}^{\circ }$
• C. angle of refraction is ${24.41}^{\circ }$
• D. angle of refraction is ${30}^{\circ }$

Answer 1

The correct option is A refraction is not possible

For a ray of light travelling from diamond to glass, the critical angle is given by,
$\sin {\theta }_c=\frac{1}{{\mu }_d}=\frac{1}{2.42}$

$\sin {\theta }_c\approx 0.4\Rightarrow {\theta }_c<{30}^{\circ }(\because \sin {30}^{\circ }=0.5)$

It is given that $i={30}^{\circ }$.
As $i>{\theta }_c$, the ray of light will undergo total internal reflection.

Hence, $\left(C\right)$ is the correct answer.