The speed of light in vacuum is \(3 \times 10^8\) m/s. The absolute refractive index of glass is 1.5 and that of water is 1.33. Find (a) the speed of light in glass, (b) the speed of light in water, (c) the refractive index of glass with respect to w…

Answer: (a) \(2 \times 10^8\) m/s; (b) about \(2.26 \times 10^8\) m/s; (c) about 1.13.

Absolute refractive index \(n = \dfrac{c}{v}\), so \(v = \dfrac{c}{n}\).

(a) \[v_g = \frac{3 \times 10^8}{1.5} = 2 \times 10^8\ \text{m/s}\]

(b) \[v_w = \frac{3 \times 10^8}{1.33} \approx 2.26 \times 10^8\ \text{m/s}\]

(c) \[n_{gw} = \frac{n_g}{n_w} = \frac{1.5}{1.33} \approx 1.13\]

(Equivalently, \(n_{gw} = v_w / v_g = 2.26/2 \approx 1.13\).) The refractive index is a ratio of speeds, so it has no unit.