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 an unpolarised 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 polarising angle.

Since,

Polarisation of reflection, the reflected light gets completely plane polarised and which makes angle \(frac{pi }{2}\) 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

\(frac{sin i}{sin }=mu\)

Where

i = ip and

r = 90° – ip

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

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