Polarisation

prashantThis article has been authored by Prashant Sharma, a Technology Columnist-Engineer by Profession who has scripted a cluster of Utility focussed and simplistic write-ups relating to Physics out here. His fundamental striking articles at XAmplified are easy-to-understand and helpful enough for Physics-phobic folks

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:

Two Waves are expressed

Resultant wave is given by,

Resultant Wave

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.

Two Linearly Polarized Waves

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

Time Variation of Resultant Electric Field

Equation (7) may be expressed as,

Expressed Equation

Using equation (6), we have

Expressed Equation

After Squaring we get,

After Squaring

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

Special cases


Plane polarized light

Dell

then equation (9) becomes

For Plane Polarized Light

Elliptically polarized light

For Elliptically polarized light

Where, n = 1, 2, 3, ….

Then,

Eq.

So, that equations gives

Eq.

Thus under this condition then emergent light is elliptically polarized.

Circularly polarized light

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

Circularly polarized light

When

Eq.

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.