Question

A ray of light is incident from air into diamond at the surface with an angle of 70 degree. what is the angle it makes in the diamond if the refraction index of diamond is 2.42.​

Answer 1

Answer: Angle is 18.66°

Step-by-step explanation: When an incident light passes through two different media, the ray of light is refracted. Refraction is the bending of the light that happens when the wave changes its velocity while passing through a different surface.

The incident light makes an angle with the normal to the surface at a point. This angle is called Angle of Incidence. After going through the other medium, the wave makes a different angle with the normal. That angle is called Angle of Refraction.

Light changes velocity when passing through different media because each material has different index of refraction. For air, index of refraction is n = 1.

The incident angle, the refracted angle and index of refraction is related by the following formula, known as Snell's Law:

`n_(1)sin\theta_(1)=n_(2)sin\theta_(2)`

where

n₁ is index of refraction of the incident medium

θ₁ is angle of incidence

n₂ is index of refration of the refracted medium

θ₂ is angle of refraction

For the ray of light incident from air into a diamond, the angle of refraction is

`sin\theta_(2)=(n_(1)sin\theta_(1))/(n_(2))`

`sin\theta_(2)=(1*sin70)/(2.42)`

`sin\theta_(2)=0.32`

`\theta_(2)=arcsin 0.32`

`\theta_(2)=` 18.66

The angle light makes in the diamond is 18.66°.