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Last updated date: 27th Nov 2023
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MVSAT Dec 2023

A beam of light travelling in water falls on a glass plate immersed in water. When the incidence angle is \[51^\circ \] , then the reflected beam of light is found polarized.Calculate \[\mu \] of glass. Given \[\mu \] of water is \[\dfrac{4}{3}\] .

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Hint: The incident and reflected rays forms two angles at the point of incidence: the angle of incidence and the angle of reflection. The angle of incidence is an angle formed at the point of incidence between the normal and the incident ray.

Complete step by step answer:
As light or other waves pass through a boundary between two different isotropic media, such as water, glass, or air, Snell's law is a formula used to describe the relationship between the angles of incidence and refraction. The reciprocal of the indices of refraction, or the ratio of the sine of the angles of the incidence and refraction, is equal to the ratio of phase velocities in the two media, according to Snell's law:
\[\dfrac{{\sin {\theta _2}}}{{\sin {\theta _1}}} = \dfrac{{{\nu _2}}}{{{\nu _1}}} = \dfrac{{{n_1}}}{{{n_2}}}\]
with each \[\theta \] representing the angle measured from the boundary's natural, \[\nu \] representing the velocity of light in the respective medium, and \[n\] representing the refractive index of the respective medium.

Brewster's angle, also called the polarization angle, is the angle of incidence at which light of a specific polarization is perfectly transmitted through a transparent dielectric surface with no reflection. Brewster's angle can be derived using Snell’s law,
\[{\mu _{water}}\sin {\theta _1} = {\mu _{glass}}\sin {\theta _2} \\
\Rightarrow {\mu _{water}}\sin {\theta _1} = {\mu _{glass}}\cos {\theta _1}\]
since reflected light would be \[100\% \] polarised if it is reflected at a \[90^\circ \] angle to the refracted light.
\[tan \theta = \dfrac{{{\mu _{glass}}}}{{{\mu _{water}}}}\]
Given that, \[\theta = 51^\circ \] and \[{\mu _{water}} = \dfrac{4}{3}\] .
We want to calculate the \[\mu \] of glass.
Therefore, by rearranging the formula, we got
\[{\mu _{glass}} = \tan \theta \times {\mu _{water}}\]
We find that \[\tan \theta = \tan 51^\circ = 1.2349\]
Therefore, after substituting the values
\[{\mu _{glass}} = 1.2349 \times \dfrac{4}{3} \\
\therefore {\mu _{glass}}= 1.647\]

Hence, the answer is \[{\mu _{glass}} = 1.647\].

Note: Snell's law is used to calculate the path of light rays passing through refractive media with different refractive indices. Only isotropic or specular media, such as glass, are generally valid.Snell’s law has a wide range of applications in physics especially in the branch of optics. It is used in optical apparatus such as eyeglasses, contact lenses, cameras, rainbows.