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 $2\times {10}^{8}m/s$ find the speed of light in water.

Answer 1

${}_a{n}_g=\frac{2}{3}{}^{}{}_w{n}_a=\frac{4}{3}{v}_g=2\times {10}^{8}m/s$
Since, ${}_a{n}_g=\frac{v_g}{v_a}=\frac{2}{3}$
$v_a=\frac{3\times 2\times {10}^8}{2}{v}_a=3\times {10}^{8}m/s$
Now, ${}_w{n}_a=\frac{v_a}{v_w}=\frac{4}{3}$
$v_w=\frac{3\times 3\times {10}^8}{4}{v}_w=2.25\times {10}^{8}m/s$