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Question

A beam of unpolarized light is incident on an air-glass interface derive, using a suitable ray diagram that light reflected from the interface is completely polarised, when tanip=?


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Solution

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Step 1: Given data

When unpolarized 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 a polarizing angle.

The reflected light is completely plane polarised.

Let ip be the polarising angle.

Let r be the angle of refraction.

Let the refractive index of air be μ1=1.

Let the refractive index of glass be μ2=μ.

Therefore, the reflected ray and refracted ray are perpendicular to each other.

Step 2: Formula Used

According to Brewster’s law,

ip+r=90°

r=90°ip

According to Snell’s law

μ1sini=μ2sinr

μ=sinisinr

Step 3: Brewster's Angle

Upon substituting the values we get,

μ=sinipsin90°-ip

μ=sinipcosip

μ=tanip

This relation is known as the Brewster angle.


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