Question

(a) State the laws of refraction of light. Give an expression to relate the absolute refractive index of a medium with speed of light in vacuum.

(b) The refractive indices of water and glass with respect to air are $\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ and $\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ respectively. If the speed of light in glass is $2\times {10}^{8}m{s}^{-1}$, find the speed of light in (i) air, (ii) water.

Answer 1

(a)

1. Refractive index is defined as the ratio of the speed of light in a vacuum to its speed in a specific medium.
2. Mathematically, refractive index (n) = $\frac{speedoflightinvacuum}{speedlightinmedium}=\frac{c}{v}$.
3. Refractive index is a unitless quantity.
4. In terms of angle of incidence (i) and angle of refraction (r), $n=\frac{\sin i}{\sin r}$.

(b)

Step 1: Given data

1. Refractive index of water $n_w=\frac{4}{3}$
2. Refractive index of glass $n_g=\frac{3}{2}$
3. Speed of light in the glass $=2\times {10}^{8}m{s}^{-1}$

Step 2: Formula and calculation of speed of light in air

$n_g=\frac{c}{v_g}$, where $v_g$ is the speed of light in the glass

$$\begin{gathered} v_g=\frac{c}{n_g} \\ c=\frac{2\times {10}^8\times 3}{2} \\ =3\times {10}^{8}m{s}^{-1} \end{gathered}$$

Hence, the speed of light in air is $3\times {10}^{8}m{s}^{-1}$.

Step 3: Formula and calculation of speed of light in water

$n_w=\frac{c}{v_w}$, where $v_w$ is the speed of light in water

$$\begin{gathered} v_w=\frac{c}{n_w} \\ {v}_w=\frac{3\times {10}^8\times 3}{4} \\ =2.25\times {10}^{8}m{s}^{-1} \end{gathered}$$