Brewster Angle Polarization

In 1811, Brewster performed a number of experiments to study the polarization of light by reflection at the surfaces of different media.

He found that ordinary light is completely polarized in the plane of incidence when it gets itself reflected from a transparent medium at a particular angle known as the angle of polarization.

He was able to prove that the tangent of the angle of polarization is numerically equal tot eh refractive index of the medium. Moreover, the reflected and the refracted rays are perpendicular to each other.

Suppose the unpolarized light is incident at an angle equal to the polarizing angle on the glass surface. It is reflected along BC and refracted along BD.

From Snell’s law,

=sin i/sin r                                 (i)

From Brewster’s law

= tan i = sin i/cos i                   (ii)

Comparing (i) and (ii)

cos i = sin r = cos (π/2- r)

∴ i = π/2- r, or i + r = π/2

As, i + r = π/2 ,  ∠CBD is also equal to π/2. Therefore, the reflected and the refracted rays are at right angles to each other.

From Brewster’s law, it is clear that for crown glass of refraction index 1.52, the value of i is given by

i = tan-1 (1.52) or i = 56.7˚

However, 57˚ is an approximate value for the polarizing angle for ordinary glass. For a refractive index of 1.7 the polarizing angle is about 59.5˚ i.e. the polarizing angle is not widely different for different glasses.

As the refractive index of a substance varies with the wavelength of the incident light the polarizing angle will be different for light of different wavelengths. Therefore, polarization will be complete only for light of a particular wavelength at a time i.e. for monochromatic light.

It is clear that the light vibrating in the plane of incidence is not reflected along BC. In the reflected beam the vibrations along BC cannot be observed whereas vibrations at right angles to the plane of incidence can contribute for the resultant intensity. Thus, we get plane-polarized light along BC. The refracted ray will have both the vibrations (i) in the plane of incidence and (ii) at right angles to the plane of incidence. But it is richer in vibrations in the plane of incidence. Hence it is partially plane-polarized.

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