In an experiment to measure the index of refraction of human...

In an experiment to measure the index of refraction of human skin, it was found that if a beam of unpolarized light was shone on a skin sample from air at an incident angle of $54.7^{\circ},$ the reflected light was completely polarized. What is the index of refraction of this skin sample?

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Key Concepts

Brewster’s Angle

Brewster’s angle is the specific angle of incidence at which light reflected from a surface is completely polarized perpendicular to the plane of incidence. This phenomenon occurs because, at this angle, the reflected and refracted beams are perpendicular to each other, and it is described by the relation tan(theta_B) = n, where theta_B is Brewster’s angle and n is the index of refraction of the medium.

Index of Refraction

The index of refraction is a fundamental optical property that quantifies how much the speed of light is reduced in a material compared to its speed in a vacuum or air. It is used to characterize the material's optical response and is calculated using relationships such as the one involving Brewster’s angle, where n = tan(theta_B).

Polarization of Light

Polarization of light refers to the orientation of the electric field vector in the electromagnetic wave. When unpolarized light strikes a surface at Brewster’s angle, the reflected light becomes completely polarized, meaning the light waves oscillate in only one direction, providing a diagnostic feature in optical experiments.

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