# A beam of unpolarised light is incident on a air-glass interface derive, using a suitable ray diagram that light reflected from the interface is completely polarised, when tan ip = ??

When an unpolarised light is incident on air-glass interface and some of the light reflected back to medium, some of the light refracts through the air-glass interface may be completely polarised (or) partially polarised (or) it can be unpolarised also it depends upon the angle of incidence for the angle of incidence of \((theta )=0{}^circ ,and,90{}^circ\) the reflected light remains unpolarised.

The angle of incidence at which the reflected light is completely plane polarised is known as polarization angle (or) Brewster’s angle.

When un polarised light is incident on the interface of Air-glass interface, the reflected light is polarised with its electric vector perpendicular to the plane of incidence. When the reflected and refracted light rays makes 90° with each other this angle of incidence is known as Brewster’s angle (or) angle of polarization. Refer the diagram

ip + r = 90°

from Snell’s law

μ1 sin i = μ2 = sin r

μ1 sin ip = μ2 sin r

where μ1 = 1 and μ2 = μ

ip + r = 90°

r = 90° – ip

sin ip = μ sin (90° – ip)

sin ip = μ cos ip

\(frac{sin {{i}_{p}}}{cos {{i}_{p}}}=mu\)

tan ip = μ

hence condition for polarization is proved.