Total internal reflection is an optical phenomenon in which waves arriving at the interface of two medias are not refracted to the second media but is completely reflected back to the first media. It occurs when a wave travels from a denser medium to a rarer medium, i.e. the second medium has a lower refractive index when compared to the first medium.

Critical angle (θ_c) is the minimum angle of incidence of an optical wave for which the total internal reflection occurs for that wave. It is given by,

Here n₁ and n₂ are the refractive indices of the two medias. Where n₁ is the denser medium and n₂ is the rarer medium.

When a ray of light is incident from a denser medium to a rarer medium, it gets refracted to the second medium. As we go on increasing the incident angle, the angle of refraction also increases according to the Snell’s law of refraction. This reaches a limit where the refracted ray passes through the surface of the second medium, i.e. the angle of refraction becomes 90°. On further increasing the incident angle, the rays are reflected back to the first media and this phenomenon is known as total internal reflection. The minimum angle of incidence at which the rays are reflected back to the first surface or the phenomena of total internal reflection occur is known as the critical angle.

Applying Snell’s law to the interface of the two media, we get,

When incident angle approaches the critical angle, the refraction angle becomes 90°, i.e. θ₁=θ_c and θ₂=90°.

So the above equation becomes,

So we get,