Question

Let the $x-z$ plane be the boundary between two transparent media. Medium 1 in $z \geq 0$ has a refractive index of $\sqrt{2}$ and medium 2 with $z<0$ has a refractive index of $\sqrt{3}$. A ray of light in medium 1 given by the vector $\vec{A}=6 \sqrt{3} \hat{i}+8 \sqrt{3} \hat{j}-10 \hat{k}$ is incident on the plane of separation. The angle of refraction in medium 2 is

• A. $75^{\circ}$
• B. $30^{\circ}$
• C. $45^{\circ}$
• D. $60^{\circ}$

Answer 1

Answer: (C)

The data is inconsistant
Taking boundary as $x-y$ plane instead of $x-z$ plane, the angle of incidence is given as
$\cos \theta =\frac{(-\widehat{k}) \cdot(6 \sqrt{3} \hat{i}+8 \sqrt{3} \hat{j}-10 \hat{k})}{\sqrt{108+192+100}} $
$=\frac{1}{2} \Rightarrow \theta=60^{\circ}$
Now, $\sqrt{2} \sin 60^{\circ}=\sqrt{3} \sin r$
$\Rightarrow \sin r=\frac{1}{\sqrt{2}} $
$\Rightarrow r=45^{\circ}$