(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 4/3 and 3/2 respectively. If the speed of light in glass is $2 \times 10^8$ $ms^{-1}$, find the speed of light in (i) air, (ii) water.

(a) Laws of Refraction of Light:

1. The incident ray, the refracted ray, and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.
2. The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant, for the light of a given colour and for the given pair of media. This is also known as Snell's law of refraction:

$$\frac{\sin i}{\sin r} = \text{constant}$$

Expression for Absolute Refractive Index:

The absolute refractive index of a medium ($n_m$) is defined as the ratio of the speed of light in vacuum ($c$) to the speed of light in that medium ($v$):

$$n_m = \frac{c}{v}$$

(b) Numerical Calculations:

Given:

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

(i) Speed of light in air (vacuum), $c$:

Using the relation $n_g = \frac{c}{v_g}$:

$$c = n_g \times v_g = \frac{3}{2} \times (2 \times 10^8 \text{ m s}^{-1}) = 3 \times 10^8 \text{ m s}^{-1}$$

(ii) Speed of light in water, $v_w$:

Using the relation $n_w = \frac{c}{v_w}$:

$$v_w = \frac{c}{n_w} = \frac{3 \times 10^8 \text{ m s}^{-1}}{\frac{4}{3}} = \frac{9}{4} \times 10^8 \text{ m s}^{-1} = 2.25 \times 10^8 \text{ m s}^{-1}$$