#### Polarization

The phenomena of interference, diffraction, reflection and refraction are characteristics of all waves, either of transverse or of longitudinal, but the polarization is a characteristic of the transverse wave.

Polarization can be demonstrated with a string and two narrow slits as shown in the figure. One end of the string is tied at a fixed point, P and the other end is jerked up-down. The waves then pass along the string. If the slit is vertical, the wave will pass to P without disturbance. If the slit is horizontal, the displacement on the string is stopped by the slit, and the amplitude of the vibration becomes zero. So, no wave passes on the string. This shows that the wave propagation is affected by the orientation of the slit for a transverse wave. But if the wave is longitudinal, this will not affect the propagation of the wave. If the string is as shown in the figure, the wave passing out of slit is linearly polarized and the slit is called the filer which is called the filter which blocks the motion in other direction. The wave in the string is polarized in yz-direction as shown in a figure.

#### Polarisation

An ordinary light beam consists of a large number of waves emitted by the atoms of the light source. Each atom produces a wave having some particular orientation of the electrical field E as shown in the figure. The magnetic field B associated with the wave is perpendicular to the field E and both are perpendicular to the direction of propagation.PolaroidThe direction of polarization of each wave is defined by the direction in which the electric field E is vibrating. A wave is said to be linearly polarized if the resultant electric field E vibrates in the same direction at all times at particular points as shown in the figure. The wave is then called the linearly or plane polarized. The plane formed by E and the direction of propagation is called the plane of polarization of the wave.

PolaroidThe direction of polarization of each wave is defined by the direction in which the electric field E is vibrating. A wave is said to be linearly polarized if the resultant electric field E vibrates in the same direction at all times at particular points as shown in the figure. The wave is then called the linearly or plane polarized. The plane formed by E and the direction of propagation is called the plane of polarization of the wave.

A Polaroid is a device used to produce a plane polarized light. It consists of a long chain of molecules aligned in a particular direction. Polaroid is made from crystals of iodosuphide of quinine in thin sheet mounted between two thin sheets of glass or cellulose. These crystals are also called herapathide. Polaroid has variety of uses in a daily life:

1. Polaroids are used as polarizing sunglasses because the light passing through such sunglasses is plane polarized and less intense by polaroids.
2. Polaroids are used as glass windows in trains and airplanes. One of the polaroids is fixed while the other can be rotated to have the desired intensity of light.
3. Polaroids are used to eliminate the dazzle from the headlights of cars, buses and other vehicles.
4. Polaroids are used to record and three dimensional moving pictures.
5. Polaroid laser beams are used to needles for producing sound from compact disks in CDs players.
6. Liquid crystal display (or LCD) in calculators, watches etc. use the principle of polarization to form numbers and letters.
7. The microscopes fitted with polaroids enables to see very minute particles which are not seen properly due to the glare of light.

#### Polarization by Selective Absorption

The Polaroid polarizes light through selective absorption by the oriented molecules. In an ideal polarizer, the light with vector E parallel to the transmission axis is transmitted and light with E perpendicular to the transmission axis is completely absorbed as shown in the figure.

An analyser is set with its axis making an angle θ with polarizer axis, and it intercepts the polarized beam. If Eo cos θand light is polarized again along the axis of analyser. Since the intensity of the transmitted beam varies as square of its amplitude, the intensity of polarized beam transmitted through the analyser is

$$I = I_m\cos ^2\theta$$

where I_m is an intensity of polarized light incident on an analyser. This law is called Malus law.

Transverse Nature of light (experimental verification)

The figure shows an unpolarized light beam incident on a Polaroid P. It is found that the intensity of the transmitted light through P is reduced to half the intensity of incident light.

#### Polarization by Reflection

When an unpolarized light beam is an incident on a transparent material, such as water, glass, etc., the reflected and refracted beam are partially polarized. Each electric field vector is resolved into two components, one parallel to the surface, represented by dots and the other represented by an arrow, both being perpendicular to the direction of propagation.

When the angle of incident is increased, the polarization in reflected beam increases, and at a particular angle of incidence, θp, the reflected beam is completely plane polarized with electric field vector parallel to the reflecting surface. The angle of incidence at which the complete polarization occurs is called polarizing angle θp, the angle between reflected and refracted beam is 90o. We have

\begin{align*} \theta _p + 90^o + \theta &= 180 ^o \\ \text {or,} \: \theta _p + \theta &= 90^o \\ \text {or,} \: \theta &= 90^o - \theta _p \end{align*}

Using Snell’s law of refraction, the refractive index of the material is

\begin{align*} \mu &= \frac {\sin i}{\sin r} = \frac {\sin \theta _p}{\sin \theta } \\ \text {But} \: \sin \theta = \sin (90 - \theta _p) = \cos \theta _p, \: \text {and} \\ \mu &= \frac {\sin \theta _p}{\cos \theta _p} = \tan \theta _p \\ \therefore \mu &= \tan \theta _p \\ \end{align*}

This expression is called Brewster’s law and sometime θp, is called Brewster’s angle. Brewster’s law states that the tangent of polarizing angle is equal to the refractive index of the material. Since µ varies with wavelength of light, so polarizing angleθp, is also the function of wavelength.

Reference

Manu Kumar Khatry, Manoj Kumar Thapa, Bhesha Raj Adhikari, Arjun Kumar Gautam, Parashu Ram Poudel. Principle of Physics. Kathmandu: Ayam publication PVT LTD, 2010.

S.K. Gautam, J.M. Pradhan. A text Book of Physics. Kathmandu: Surya Publication, 2003.

The phenomena of interference, diffraction, reflection and refraction are characteristics of all waves, either of transverse or of longitudinal, but the polarization is a characteristic of the transverse wave.

A Polaroid is a device used to produce a plane polarized light.

The Polaroid polarizes light through selective absorption by the oriented molecules.

Brewster’s law states that the tangent of polarizing angle is equal to the refractive index of the material.

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