Question

If a light ray from air enters three different media in such a way that the refracted angles are ${45}^0$, ${30}^0$ and ${60}^0$ respectively. Identify the medium where the speed of light is the lowest.

• A. Medium 1
• B. Medium 2
• C. Medium 3
• D. Same for all

Answer 1

The correct option is B Medium 2

Angle of incidence $\left(i\right)$ is same for all three media. Angle of refraction for the different media are:
$r_{m1}={45}^{\circ }$
$r_{m2}={30}^{\circ }$
$r_{m3}={60}^{\circ }$
According to Snell’s law, we know that
$\Rightarrow$ $n$ = $\frac{sini}{sinr}$ = $\frac{v_1}{v_2}$
$\Rightarrow$ $v_2$ = $v_1$$\times \frac{sinr}{sini}$
Since, $i$ and $v_1$ are constant in all the three scenarios,
$\Rightarrow$ $v_2$ = $sinr$
$\Rightarrow$Lesser the $r$, less will be the speed of light in that medium.
Since, $r$ is lowest in medium $2$, hence, light will travel with the lowest speed in medium $2$.