## Polarisation

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Table Of Content

## Phenomena

According to the electromagnetic theory of light, a light wave consists of electric and magnetic vectors vibrating in mutually perpendicular directions both being perpendicular to the direction of propagation of light.

## Types of Polarised Light

It majorly comprises of :

1. Plane polarized light
2. Circularly polarized light
3. Elliptically polarized light

In Linearly polarized light, the light vector vibrates simple harmonically along a straight line perpendicular to direction of propagation of light i.e., the orientation of light vector remains unchanged while its magnitude undergoes a change during vibrations. When two plane polarized waves are superimposed then under certain conditions, the resultant light vector may rotate. The magnitude of the resultant light vector remains constant while its orientation varies regularly, the tip of  the vector traces a circle and light will be Circularly polarized. If however, both magnitude and orientation of light vector vary, the tip of the vector traces ellipse and light is said to be Elliptically polarized.

## Mathematical Explanation of Polarisation

1. The electric vectors of waves oscillating along same axis
Let us consider two linearly polarized waves with their electric vectors oscillating along X – axis. Then waves are expressed as:

Resultant wave is given by,

2. The electric vector of waves oscillating along perpendicular axes:

Let us now consider two linearly polarized waves propagating along z – axis put with their electric vectors along two mutually perpendicular directions.

In order to find resultant disturbance, we consider the time variation of resultant electric field.

Equation (7) may be expressed as,

Using equation (6), we have

After Squaring we get,

The resultant of two plane polarized beams whose electric vectors oscillate in perpendicular directions is in general, elliptically polarized.

## Special cases

### Plane polarized light

then equation (9) becomes

### Elliptically polarized light

Where, n = 1, 2, 3, ….

Then,

So, that equations gives

Thus under this condition then emergent light is elliptically polarized.

### Circularly polarized light

When a = b and the thickness of plate is such that

When

the resulting vibration is a slant ellipse.

Thus it is obvious that the plane polarized and circularly polarized lights are the special cases of elliptically polarized light.