## Note on Transverse Nature of Light, Polarisation by Selective Absorption and by Refraction

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#### Transverse Nature of Light

Experimental Verification

The figure shows an unpolarized light beam on Polaroid P. It is the intensity of the transmitted light through P is reduced to half the intensity of incident light. When another Polaroid A is set with its axis parallel to the axis of P, the transmitted light through A has no change in intensity. When the axis of A is gradually rotated to the axis of P, the intensity of light transmitted through A gradually decreases and finally becomes zero as the two axes cross each other. Then no light is obtained through A.

This experiment showed that when a unpolarised light is an incident on the Polaroid P, the transmitted light has electric vector vibrating parallel to the transmission axis of P while the electric vector vibrating perpendicular to the transmission axis is absorbed. So the light transmitted through P has electric vector parallel to its axis only and the Polaroid P has made vibrations of light in one direction. The phenomenon of restricting the vibration of light in one direction is called polarization of light. Polaroid P is called polarizer.

When the pass-axis of the Polaroid A is parallel to the direction of the vibrations of the plane polarized light, this polarized light is transmitted as such by the Polaroid A.

When the axis of the Polaroid A is perpendicular to the direction of vibrations of the plane polarized light, then the vibrations of the plane polarized light is completely blocked. So, there is no light transmitted through the Polaroid A and hence the intensity of light transmitted is zero. The Polaroid A identifies the polarization of light and hence it is known as an analyzer.

#### Polarization by Selective Absorption

A polarized light can be obtained by using a material which transmits waves whose electric fields vibrate in a plane parallel to a certain direction of orientation and absorbs waves whose electric fields vibrate in all other directions. Such materials are called polaroids and are fabricated in thin sheets of long chain hydrocarbons. In an ideal polarizer, the light with vector E parallel to transmission axis is transmitted and light with E perpendicular to the transmission axis is completely absorbed as shown in the figure.

The figure shows an unpolarised light beam incident on a polarizer. Since the axis of the polariser is oriented vertically, the light through it is polarized vertically. An analyser is set with its axis making an angle $$\theta$$ with polarizer axis, and it intercepts the polarized beam. If E0 is the electric field of a vector of the transmitted beam, the component of E0 perpendicular to the analyser axis is completely absorbed and the component parallel to analyser axis is allowed to pass through it. This component is E0 cos θand 'f'light is polarized again along the axis of an 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 Im is an intensity of polarized light incident on the analyser. This law is called Malus law and applies to any two polarizing materials whose transmission axes are at an angle Ï´ to each other. According to this law, the intensity is maximum if the transmission axes are parallel and intensity is zero if the transmission axes are perpendicular to each other.

#### Polarisation by Refraction

When an unpolarised 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 vectors is resolved into two components, one parallel to the surface, represented by dots and the other represented by an arrow, the both being perpendicular to each other and 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 the polarizing angleθp. The refracted wave is however partially polarized as shown in figure. Brewster found that at polarizing angle θp, the angle between reflected and refracted beam is 90o. From figure 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 θpis 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 angle θpis also the function of wavelength.

The phenomenon of restricting the vibration of light in one direction is called polarization of light.

A polarized light can be obtained by using a material which transmits waves whose electric fields vibrate in a plane parallel to a certain direction of orientation and absorbs waves whose electric fields vibrate in all other directions.

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

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