A ray of monochromatic light is incident on the plane surface of separation between two media $X$ and $Y$ with 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 $V_x$ and $V_{\mathrm{Y}}$ are the velocities of the ray in media $X$ and $Y$ respectively, then which of the following is true?

Question

A ray of monochromatic light is incident on the plane surface of separation between two media $X$ and $Y$ with 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 $V_x$ and $V_{\mathrm{Y}}$ are the velocities of the ray in media $X$ and $Y$ respectively, then which of the following is true?, $V_X=\frac{1}{\sqrt{3}} V_Y$, $\mathrm{V}_{\mathrm{X}}=\sqrt{3} \mathrm{~V}_Y$, Total internal reflection can happen when the light is incident in medium $X$., $v_X=\sqrt{3} v_Y$, where $v_X$ and $v_Y$ are frequencies of the light in medium $X$ and $Y$ respectively.

MARKS App · Accepted Answer

Hint : $\begin{aligned} & \mu_1 \sin i=\mu_2 \sin r \ & \frac{C}{V_X} \sin i=\frac{C}{V_Y} \sin r \ & \frac{\sin i}{\sin r}=\frac{V_X}{V_Y}=\sqrt{3} \ & V_Y=\frac{V_X}{\sqrt{3}} \ & V_X=\sqrt{3} V_Y\end{aligned}$ $y=m x$ $\sin r=\left(\tan 30^{\circ}\right) \sin \mathrm{i}$ $\frac{\sin i}{\sin r}=\frac{1}{\tan 30^{\circ}}=\frac{\sqrt{3}}{1}$

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