Question

The absolute refractive indices of water and glass are $\frac{4}{3}$ and $\frac{3}{2}$ respectively. If the speed of light in glass is $2 \times 10^8$ m/s, find the speed of light in (i) water and (ii) vacuum.

Hint:

Use $n = \frac{c}{v}$ for calculations.

Answer 1

Given: \[ n_g = \frac{3}{2} = 1.5, \quad v_g = 2 \times 10^8 \text{ m/s} \] Speed of light in vacuum: \[ c = n_g \times v_g = 1.5 \times 2 \times 10^8 = 3 \times 10^8 \text{ m/s} \] Speed of light in water: \[ v_w = \frac{c}{n_w} = \frac{3 \times 10^8}{1.33} \approx 2.26 \times 10^8 \text{ m/s} \] So, (i) Speed in water = $2.26 \times 10^8$ m/s (ii) Speed in vacuum = $3 \times 10^8$ m/s