Question

The refractive indices of glass and water with respect to air are $\frac{3}{2}$ and $\frac{4}{3}$ respectively. If the speed of light in glass is \(2 \times 108~

m/s\). Find the speed of light in water.

Answer 1

Let the speed of light in air be x
Refractive index of glass $=\frac{speedoflightinair}{speedoflightinglass}$
$\frac{3}{2}=\frac{x}{2}\times {10}^{8}m{s}^{-1}$
$X=3\times 2\times {10}^{8}m{s}^{-1}$
Speed of light in air $=3\times {10}^{8}m{s}^{-1}$
2.Water
Refractive index of water $=\frac{speedoflightinair}{speedoflightinwater}$
$\frac{4}{3}=\frac{3\times {10}^{8}m{s}^{-1}}{speedoflightinwater}$
Speed of light in water $=3\times {10}^{8}m{s}^{-1}\times \frac{3}{4}$
Speed of light in water $=9\times {10}^{8}m{s}^{-1}\times 4$
Speed of light in water $=2.2\times {10}^{8}m{s}^{-1}$