A ray of light is incident on the face AB of a prism at a small angle to the normal and emerges through the face BC. The incident angle is slowly reduced. If the ray of light strikes AB normally then no light emerges through BC at all. This is the initial position so that no light emerges through BC. The angle ABC is 40^{0}. What is the refractive index of the material of the prism?

###### Solution.

When light goes from a denser medium to a less dense medium, there is a critical angle of incidence above which all light is reflected. This phenomenon is called total internal reflection.

The Snell’s law will have the following form

sin(θ_{c})=n_{2}/n_{1}

where θ_{c} – critical angle, n_{1} – refractive index of the denser medium and n_{2} – refractive index of the less dense medium.

In our case, n_{2} equals 1 (refractive index of air) and also, θ_{c} equals to the angle ABC.

Thereby,

n_{1} = 1/sin(θ_{c})

or

n_{1} = 1/sin(40^{0}) ≈ 1.56