Polarised Waves

The above diagram shows the two corresponding fields that form Electromagnetic Radiation, such as Light. 

The Electric field oscillates in the (horizontal)  XZ plane

The Magnetic field oscillates in the (vertical) XY plane

As each field operates in only one plane, each field is referred to as being linearly Polarised. 

Note - An example of polarisation of this type is TV aerials. The aerial is set up so that it  emits/detects the oscillation of the Electric field in the vertical plane, and if the aerial is not oriented correctly, reduced signal is detected.  

Unpolarised Waves

If the source of the EM-waves is a source such as a filament bulb, then the light is made up of light given out by the random changes within the atoms, and as such the resultant waves are at random angles to each other. The resultant light would be unpolarised.

Note - Only transverse waves can be polarised. 

Polarisation using Filters

In 1852, William Bird Herapath found that urine of a dog that had been fed Quinine formed crystals of iodo-quinine sulphate that absorbed light of almost all polarisations but allowed through one specific angle. 

In 1938, Edwin Land patented the material Polaroid which embedded the crystals into a plastic sheet, allowing for many different applications. 

The above diagram shows how a Polariser blocks most of the unpolarised light, only allowing a specific polarisation to pass through.

Note - The polarisation that can pass through the polariser is perpendicular to lines/bars that make up the Polariser. This is because the line/bars make the object reflective in that plane, so transmission only occurs when at right angles. 

If two separate polarisers are used at a rotation of 90o to each other, then all transmission is blocked. This is explained in the following diagram :-

In the above diagram:- 

Polariser X (Polariser) causes only light oscillating vertically to pass through it

Polariser Y (Analyser) only allows light oscillating horizontally to pass through it

With the two polarisers working against each other in this way, no light is transmitted. 

Malus' Law

So far, the discussion has focussed solely on full transmission or nothing. Malus' Law gives an explanation for angles other than 0o or 90o

In the above diagram, unpolarised  light is passed through a sheet of Polaroid, which is referred to as the Polariser.  The now polarised beam is the passed through a second sheet of Polaroid, called the Analyser. The transmission axis (the axis that allows light to pass through the Polaroid) of the Analyser is rotated through an angle of θ compared to the Polariser. 

The beam that leaves the Analyser is polarised to the same direction as the transmission axis of the Analyser. 

If the system is viewed "end on", the above diagram can be generated. As can be seen, if the incident beam has an amplitude of A0, the component of A0 that is parallel to the transmission axis of the Analyser less than A0. This gives a value for the amplitude transmitted through the Analyser of :-  

A  =  A0 cos θ 

From Higher Physics, it can be shown that the intensity of the beam (measured in Wm-2) is proportional to the square of the amplitude, allowing the derivation below :-

A    =  A0 cosθ

A2  =  ( A0 cosx )2

A2  =  A02 cos2θ

I      = I0 cos2θ

The above formula for intensity of the beam transmitted through the analyser is known as Malus' Law. 

Example 1 - 

A sheet of Polaroid is used to reduce the intensity of a beam of polarised light. What angle should the transmission axis make with the plane of polarisation of the beam to reduce the intensity by 1/2

In order to complete this question, the following must be defined :-

I0 - The original intensity of the beam

I0 / 2 - The intensity of the transmitted beam

By applying Malus' Law :-

I0 / 2  =  I0 cos2θ

cos2θ  =  1/2

cosθ  = ( 1/2 )0.5

θ =  45o

Brewster's Law of Reflection 

The Scottish scientist Sir David Brewster discovered that at a particular angle, monochromatic light being reflected was completely polarised, with an axis of polarisation parallel to the reflective surface. He also discovered that at this particular angle, the reflected ray and the refracted ray were at right angles to each other.

The angle of incidence (ip) that this occurs at is known as Brewster's Angle. 

If we apply Snell's Law to the above system, a formula for the Brewster's Angle can be derived :- 

ip - angle of incidence 

r - angle of refraction 

n - refractive index of the glass

Example 2 -

If the refractive index of Glycerol is 1.47, calculate :-

1. The polarising angle

2. The angle of refraction at Brewster's Angle 

n =  tan ip

1.47  =  tan ip

ip  =  56o

At the polarising angle (the Brewster's Angle), the following applies :-

r + ip  =  90o

r  = 90 - i

r  =  90 - 56

r  =  34o

Applications of Polarisation 

There are many different applications of Polarisation, some of which are detailed below :-

LCD Displays - An LCD screen is made of aligned crystals between a crossed Polariser and  Analyser. By applying a Voltage across the crystals, their orientation can be changed. When oriented in one direction, they allow the polarised light to pass and the screen appears blank. When oriented in a different direction, the polarised light is blocked and a black cell is seen against a lighter background. 

Polaroid Sunglasses - Sunlight when reflected from a lake or snow can cause eye-strain due to the polarised light. As most of the polarised light will be reflecting from horizontal surfaces such as lakes, puddles etc, the transmission axis of the sunglasses is set to the vertical plane to reduce these reflections. 

3D Cinema Glasses - The glasses provided at cinemas to view 3D films work through polarisation. Each lens is set with the axis of transmission at 90to each other, and as such, the light passing through 1 lens cannot pass through the other. The image on the screen is from two synchronised projectors, each showing a slightly different view. The two different views combined with the lens, give the overall effect of a 3 dimensional image. 

Saccharimetry - This technique is used to measure the concentration of optically active  materials (which rotate the plane of polarisation) such as sugar solutions. By measuring the amount of rotation caused by the solution, its concentration can be found.

Photo-elastic Strain Analysis  - Photo-elastic materials ( eg glass, plastic ) are materials which show Birefringence  (the splitting of an incident beam of light into two beams polarised at 90o to each other) when mechanical stress is applied to them. When placed between a crossed Polariser and Analyser, the Photo-elastic material will show bright and dark fringes with the highest concentration at points of most stress. This allows models of working mechanical parts be analysed and aid in design. 

The video below shows several examples of Photo-elastic Strain Analysis