Question

State Snells law.
Calculate the velocity of light in a glass block of refractive index $1.5$
(Velocity of light in air $=3\times {10}^{8}m{s}^{-1}$)

Answer 1

Snell's law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of phase velocities in the two mediums, or equivalent to the reciprocal of the ratio of the index of refraction

$\frac{\sin {\theta }_i}{\sin {\theta }_r}=\frac{v_2}{v_1}=\frac{n_1}{n_2}$

Where θ is the angle from the normal of the boundary and $v$ is the velocity of light in the respective medium and λ is the wave length of the light in the medium and n is the refractive index of the medium.

Given that,

Refractive index of glass block $n_2=1.5$

Refractive index of air $n_1=1$

Velocity of light in air, $v_1=c=3\times {10}^{8}m/s$

We know that,

$\frac{n_2}{n_1}=\frac{c}{v}$

$\frac{1.5}{1}=\frac{3\times {10}^8}{v_2}$

$v_2=\frac{3\times {10}^8}{1.5}$

$v_2=2\times {10}^{8}m/s$

Hence, the velocity of light in a glass is $2\times {10}^{8}m/s$