Question

A ray of light is incident on the surface of separation of a medium at an angle of 45° and is refracted in the medium at an angle of 30° what will be velocity of light

Answer 1

We assume that ray of light comes from air , which is a medium where the speed of light is $3.0\times 10^8 m/s$. The light ray will get refracted, reducing the speed of light in that medium.

The equation to use in this situation is snell's law, the version which uses the difference in velocities of light in the two mediums.

We have from optics that $\frac{sin(x_i)}{sin(x_r)}=\frac{v_i}{v_r}$, where $v_i$ is the velocity in air, $v_r$ is velocity in second medium, $x_i$ is the angle of incidence and $x_r$ is the angle of refraction.

Using the information given in this question, we have that;

$\frac{sin(45)}{sin(30)}=\frac{3\times 10^8m/s}{v_r} \\=>v_r=\frac{3\times 10^8\times sin(30)}{sin(45)} \\v_r=2.12\times10^8m/s$

The velocity of light in the new medium is $2.12\times 10^8m/s$