Question

A ray of monochromatic light is incident on the plane surface of separation between two media X and Y with the angle of incidence 'i' in medium X and angle of refraction 'r' in medium Y. The given graph shows the relation between sin i and sin r. If Vx and Vy are the velocities of the ray in media X and Y respectively, Then which of the following is true?

• A. Vx=$\frac{1}{\sqrt3}$Vy
• B. Vx=$\sqrt3$Vy
• C. Total internal reflection can happen when the light is incident in medium X.
• D. Vx=$\sqrt3$Vy, where Vx and Vy are frequencies of the light and medium X and Y respectively.

Answer 1

Answer: (B)

Vx=$\sqrt3$Vy

Answer 2

The correct answer is option (B): Vx=$\sqrt3$Vy

$ux\,sin\,i=uy\,sin\,r$

slope=$\frac{sin\,r}{sin\,i}=\frac{\mu_x}{\mu_y}=tan 30^{\circ}$

$\Rightarrow \mu_x=\frac{\mu_y}{\sqrt3}\Rightarrow V_x=\sqrt3V_y$