Question

Let the $x-z$ plane be the boundary between two transparent media. Medium 1 in $z\ge 0$ 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
$\cos \theta =\frac{(-\hat{k})\cdot (6\sqrt{3}\hat{i}+8\sqrt{3}\hat{j}-10\hat{k})}{\sqrt{108+192+100}}$
$=\frac{1}{2}\Rightarrow \theta =60^{\circ }$
Now, $\sqrt{2}\sin 60^{\circ }=\sqrt{3}\sin r$
$\Rightarrow \sin r=\frac{1}{\sqrt{2}}$
$\Rightarrow r=45^{\circ }$