Refraction of Light
6.0 Total internal reflection
6.0 Total internal reflection
It is the phenomenon of reflection of light into denser medium from the boundary of denser medium and rarer medium.
Two essential conditions for the phenomenon of total internal reflection are,
- Light should travel from a denser medium to a rarer medium.
- Angle of incidence in denser medium should be greater than the critical angle for the pair of media in contact.
The figure below shows the reflection and refraction of a light ray at the interface between a denser and a rarer medium, whose refractive indices are ${\mu _D}$ and ${\mu _R}$ respectively.
From Snell's law, we can write,
$$\begin{equation} \begin{aligned} {\mu _D}\sin i = {\mu _R}\sin r \\ \sin i = \frac{{{\mu _R}\sin r}}{{{\mu _D}}} \\\end{aligned} \end{equation} $$
For total internal reflection,
$$r = 90^\circ {\text{and}}\quad i = {\theta _c}$$ or $$\sin r = 1$$
So, $$\sin {\theta _c} = \frac{{{\mu _R}}}{{{\mu _D}}}$$ or $${\theta _c} = {\sin ^{ - 1}}\left( {\frac{{{\mu _R}}}{{{\mu _D}}}} \right)$$
Here, ${\theta _c}$ is known as critical angle.
