Question

A ray of mono chromatic light is incident on the plane surface of separation between two media $x$ and $y$ with angle of incident $i$ in the medium $y$. The graph shows the relation between $\sin i$ and $\sin r$ (where $r$ is angle of refraction). The total internal reflection can take place when the incidence is in medium

• A. $x$
• B. $y$
• C. both $x$ and $y$
• D. Insufficient

Answer 1

The correct option is B $y$


Applying Snell's law at the interface,
$\frac{\sin i}{\sin r}=\frac{{\mu }_2}{{\mu }_1}....\left(i\right)$

The slope of graph $\sin r$ vs $\sin i$ is,
$\tan {30}^{\circ }=\frac{\sin r}{\sin i}$
$\Rightarrow \cot {30}^{\circ }=\frac{\sin i}{\sin r}....\left(ii\right)$

From equations $\left(i\right)$ and $\left(ii\right)$,
$\Rightarrow \cot {30}^{\circ }=\frac{{\mu }_2}{{\mu }_1}$
Or, ${\mu }_2=\sqrt{3}{\mu }_1$
$\therefore {\mu }_2>{\mu }_1$

Hence, medium $y$ is denser and medium $x$ is rarer.
For total internal reflection, light should travel from optical denser medium (medium $y$) to optical rarer medium (medium $x$)