1. A: Wave Phenomena
A.6 Polarisation

2. Polarisation
When a charged particle loses energy, a tiny disturbance or ripple in the surrounding electromagnetic field is created – an e-m wave.
The wave will be in the same plane as the plane of movement of the particle. If all the disturbances in a ray of light were occurring in the same plane, the light is said to be plane polarised.
In reality most sources of light produce unpolarised light because the electrons in the source move in all directions.
Electromagnetic waves
electron

3. Polaroids
A Polaroid filter (a polariser) polarises light rays. If an unpolarised ray of light passes through the filter, about 50% of its energy will be absorbed and 50% pass through.
Planes before:
Here is a simple explanation of how Polaroid filters work:
Light (and other electromagnetic radiations) consists of oscillating electric and magnetic fields. Polaroid is a type of plastic; its molecules are long chains, oriented parallel to one another. There are electrons that are free to run up and down the chains.
When the oscillating electric field is vertical, and the chains are vertical, the electrons are caused to move up and down with the same frequency. (The chains are like miniature aerials, absorbing the radiation.) At the same time, the electrons re-emit the radiation in all directions, and the result is that not much radiation passes straight through.
If the polymer chains are at right angles to the electric field, the electrons cannot move very far and thus do not absorb much energy from the wave, so it passes through. At any other angle, it is the component of the electric field perpendicular to the chains which passes through; this explains why the light dims as you rotate the filters.
Plane after:

5. The original light waves exist in many different planes
The original light waves exist in many different planes. The polarising filter only allows components of the wave in one plane to pass through.
E.g.
One wave in its original plane:
This has vertical and horizontal components:
- Wave after passing through filter with a vertical plane of polarisation (horizontal component absorbed):

6. Polarisation by Reflection
When an unpolarised ray of light is reflected off a non metallic surface, the reflected ray becomes partly polarised.
E.g. Reflections of light from cars, the sea, snow etc.
The degree of polarisation is dependant upon the angle of incidence of the light.

7. Brewster’s Angle
When light reflects off water, polarisation will be 100% when the angle of incidence is equal to Brewster’s angle (ϕ – phi). This occurs when the angle between the reflected and refracted rays is 90°. ϕ r

9. On the right hand side of the normal: ϕ + r = 90 but...
so...
but... sin (90 – ϕ) = cos ϕ
so Brewster’s angle is given by...
n2 = sin i
sin r
n = sin ϕ
sin (90 – ϕ)
This equation is known as Brewster’s law. Its immediate practical use was that it enabled the refractive index of glass to be determined by reflection rather than by refraction; the measurement of the refractive angle r by transmission is difficult. The result of this discovery was that it led to the rapid development and measurement of new optical glasses.
n = sin ϕ = tan ϕ
cos ϕ
ϕ = tan-1 n

10. E.g.
Calculate Brewster’s angle for diamond (n = 2.4).
ϕ = 67°

11. Malus’ Law
Unpolarised light of intensity I0 can be split into two parallel components which in turn may be polarised by a second polarising filter (called an analyser). The resulting intensity (I) is given by Malus’ Law:
I = I0 cos2 θ
θ = angle of rotation between the two polarisers.
I = intensity, the power per unit area (Wm-2) I0

12. E.g.
A sheet of Polaroid is used to reduce the intensity of a beam of polarised light. What angle should the transmission axis of the Polaroid make with the plane of polarisation of the beam in order to reduce the intensity of the beam by 50%?
so I = ½ I0
and I = I0 cos2 θ
 ½ I0 = I0 cos2 θ
½ = cos2 θ
cos θ = √(0.5)
θ = cos-1 √(0.5)
θ = 45°

13. Polaroid Sunglasses
You were sunglasses to protect your eyes, but the benefit of wearing them is to block glare. Glare is light that is polarised by reflection. They absorb the horizontally plane polarised glare off the snow, water, or other surfaces that would normally make you squint.

14. Stress Analysis
Glass and plastics become birefringent (double refraction) when placed under stress. When polarised white light is passed through stressed plastics and then an analyser, bright coloured lines are observed in the regions of maximum stress.
Demo in class

15. Liquid Crystal Displays (LCDs)
LCDs use a series of reflectors, polarisers, electrode plates, and liquid crystals. The liquid crystals are optically active substances that rotate the plane of polarisation of light that passes through it.
Examples:
Calculators
Watches
Screens
TVs

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Intensity I0
Intensity I

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