# A beam of unpolarised light is incident on the boundary between 2 transparent media if the reflected light is completely plane polarised, how is its direction related to the direction of corresponding refracted light?

When unpolarized light is incident on a transparent refracting medium, at a particular angle of incidence the reflected light and refracted light are perpendicular to each other that angle of incident is known as a polarizing angle.

Since,

Polarization of reflection, the reflected light gets completely plane-polarized and which makes an angle

$$\begin{array}{l}\frac{pi }{2}\end{array}$$
with the refracting light.

According to brewster’s law,

ip + r = 90°

r – is angle of refraction

ip – is polarising angle

r = 90° – ip

by snell’s law

μ1 sin i = μ2 sin r

μ1 = 1 and μ2 = μ

$$\begin{array}{l}\frac{sin i}{sin }=\mu\end{array}$$

Where

i = ip and

r = 90° – ip

$$\begin{array}{l}\frac{sin {{i}_{p}}}{sin (90{}^circ -{{i}_{p}})}=\mu\end{array}$$
$$\begin{array}{l}\frac{sin {{i}_{p}}}{cos {{i}_{p}}}=\mu\end{array}$$
$$\begin{array}{l}\tan {{i}_{p}}=\mu\end{array}$$
This relation is known as Brewster angle.