Question

They x-y plane is the boundary between two transparent media. Medium-1 with z > 0 has refractive index $\sqrt{2}$ and medium-2 with z < 0 has a refractive index $\sqrt{3}$. A ray of light in medium - 1 given by the vector $A=6\sqrt{3}\hat{i}+8\sqrt{3}\hat{j}-10\hat{k}$ is incident on the plane of separation. If the unit vector in the direction of refracted ray in medium-2 is $10\sqrt{\frac{x}{3}}$. Then $x$ is :

Answer 1

Since, the refractive index is changing only along the z-axis, therefore, the velocity will also change only along the z-direction.

Hence, the components along the x and y direction remain the same.

Along z direction,

$\frac{v_2}{v_1}=\frac{{\mu }_1}{{\mu }_2}$

Substituting for the values,

$v_2=10\times \frac{\sqrt{2}}{\sqrt{3}}$

Therefore, $x=2$.