Question

(a) State what is meant by refraction of light. State Snell's law for refraction of light and also express it mathematically. (b) The refractive indices of water and glass with respect to air are 4/3 and 3/2 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) = $\frac{sppedoflightinvacuum}{speedlightinmedium}=\frac{c}{v}$.
3. Refractive index is a unitless quantity.

Laws of refraction:

1. Incident ray, refracted ray and normal all lie in same plane.
2. The ratio of sine of angle of incidence to the sine of angle of reflection is constant and is called the refractive index. This is called Snell's law.
3. Mathematically, $n=\frac{\sin i}{\sin r}$.

(b)

Step 1: Given

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 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 speed of light in 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 speed of light in water

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