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Question:

Unpolarised light is incident from air on a plane surface of a material of refractive index μ. At a particular angle of incidence i, it is found that the reflected and refracted rays are perpendicular to each other. Which of the following options is correct for this situation?

i=sin⁻¹(1μ)

Reflected light is polarised with its electric vector perpendicular to the plane of incidence

i=tan⁻¹(μ)

Reflected light is polarised with its electric vector parallel to the plane of incidence

Solution:

When the reflected and refracted rays are perpendicular to each other, the angle of incidence is the Brewster angle (iB). At the Brewster angle, the reflected light is completely plane polarised with its electric vector perpendicular to the plane of incidence. The relationship between the Brewster angle and the refractive index is given by:

tan iB = μ

where μ is the refractive index of the material. Therefore, the angle of incidence i is equal to the Brewster angle iB, and i = tan⁻¹(μ). The reflected light is polarised with its electric vector perpendicular to the plane of incidence.