Question

For the same angle of incidence, the angles of refraction in media ${}^{\prime }{P}^{\prime }{,}^{\prime }{Q}^{\prime }{,}^{\prime }{R}^{\prime }$ and ${}^{\prime }{S}^{\prime }$ are ${50}^{\circ },{40}^{\circ },{30}^{\circ },{20}^{\circ }$ respectively. The speed of light is minimum in medium

• A. $P$
• B. $Q$
• C. $R$
• D. $S$

Answer 1

The correct option is D $S$

$\text{Refractive index}\left(\mu \right)=\frac{C\text{vacuum}}{\text{Cmedium}}$

$C=C_{\text{vacuum}}=$ speed of light in vacuum

$c_m=$ $C_{medium}$ $=$ speed of light

in medium

Sine rule

$\begin{array}{c}{\mu }_1\sin i_1={\mu }_2\sin {\gamma }_2\\ \text{(1)}\frac{\sin i_1}{\sin 50}={\left({\mu }_2\right)}_p\\ {\mu }_p=\frac{\sin i_1}{\sin 50}=\frac{c}{c_p}{\mu }_s=\frac{\sin 1_1}{\sin 20}=\frac{c}{c_R}\\ {\mu }_Q=\frac{\sin i_1}{\sin 40}=\frac{c}{c_Q}\\ {\mu }_R=\frac{\sin i_1}{\sin 30}=\frac{c}{c_S}\end{array}$

So speed of light in medium $\alpha$ Angle of refraction in medium

So medium with minimum Angle of

refraction has minimum speed of light

so(D) $s$ is the right option