Physics > Wave Optics > 4.0 Polarisation
Wave Optics
1.0 Introduction
1.1 Wavefronts
1.2 Huygens Principle
1.3 Interference of light
1.4 Intensity distribution
1.5 Phase difference
2.0 Young's double slit experiment
3.0 Diffraction of light
4.0 Polarisation
4.2 Brewster's law
1.2 Huygens Principle
1.3 Interference of light
1.4 Intensity distribution
1.5 Phase difference
According to Brewster's law, when unpolarised light is incident at polarising angle $\left( {{\theta _i}} \right)$ on an interface separating a rarer medium from a denser medium of refractive index $\mu $ such that,
$$\mu = \tan {\theta _i}$$
then the light which is reflected in the rarer medium is completely polarised. The reflected and refracted rays are perpendicular to each other.
Consider an unpolarised light is incident at an angle $\left( {{\theta _i}} \right)$ and undergoes reflection and refraction as shown in the figure.
According to Brewster's law, the reflected and refracted rays are perpendicular to each other.
From the figure we can write,
$$\begin{equation} \begin{aligned} {\theta _i} + 90^\circ + {\theta _r} = 180^\circ \\ {\theta _i} + {\theta _r} = 90^\circ \quad ...(i) \\\end{aligned} \end{equation} $$
From Snell's law,
$${\mu _1}\sin {\theta _i} = {\mu _2}\sin {\theta _r}\quad ...(ii)$$
From equation $(i)$ and $(ii)$ we get,
$$\begin{equation} \begin{aligned} {\mu _1}\sin {\theta _i} = {\mu _2}\sin \left( {90^\circ - {\theta _i}} \right) \\ {\mu _1}\sin {\theta _i} = {\mu _2}\cos {\theta _i} \\ \frac{{\sin {\theta _i}}}{{\cos {\theta _i}}} = \frac{{{\mu _2}}}{{{\mu _1}}} \\ \tan {\theta _i} = \frac{{{\mu _2}}}{{{\mu _1}}} \\\end{aligned} \end{equation} $$ or $${\theta _i} = {\tan ^{ - 1}}\left( {\frac{{{\mu _2}}}{{{\mu _1}}}} \right)$$
When the light is coming from air
$$\mu = \tan {\theta _i}$$
