7.2.2 Polarisation

• Transverse waves are waves with their displacement perpendicular to their direction of travel. These oscillations can happen in any plane perpendicular to the propagation direction
• Transverse waves can be polarised, this means:
  • Vibrations are restricted to one direction
  • These vibrations are still perpendicular to the direction of propagation/energy transfer

• The difference between unpolarised and polarised waves are shown in the diagram below

Diagram showing the displacement of unpolarised and polarised transverse waves

• Longitudinal waves (e.g. sound waves) cannot be polarised since they oscillate parallel to the direction of travel
• Waves can be polarised through a polariser or polarising filter. This only allows oscillations in a certain plane to be transmitted

Diagram showing an unpolarised and polarised wave travelling through polarisers

• Only unpolarised waves can be polarised as shown in diagram A
• When a polarised wave passes through a filter with a transmission axis perpendicular to the wave (diagram B), none of the wave will pass through
• Light can also be polarised through reflection, refraction and scattering
• An example of polarisation in everyday life is polaroid sunglasses. These reduce glare caused by sunlight for drivers to see through windows and fishermen to see beneath the water surface more clearly

ANSWER:   A

• Polarisation only occurs for transverse waves, therefore, C and D can be ruled out as sound and ultrasound are both longitudinal waves
• Waves are not polarised when diffracted, hence we can also rule out option B
• Radio waves are transverse waves - they can be polarised by a metal grid so only the waves that fit through the grid will be transmitted, therefore, A is correct

• The intensity of unpolarised light is reduced as a result of polarisation
• If unpolarised light of intensity I₀ passes through a polariser, the intensity of the transmitted polarised light falls by a half

• The first filter that the unpolarised light goes through is the polariser
• A second filter placed after the first one is known as an analyser 
  • If the analyser has the same orientation as the polariser, the light transmitted by the analyser has the same intensity as the light incident on it
  • If they have a different orientation, we must used Malus's law  

• Malus's law states that if the analyser is rotated by an angle θ with respect to the polariser, the intensity of the light transmitted by the analyser is

Malus’s law equation

• Recall that intensity is the power per unit area and measured in W m^-2
• If the analyser is rotated by 90° with respect to the polariser (θ = 90°), the intensity of the light transmitted by the analyser will be zero, since cos(90°) = 0
• Malus's law also explains why, if the polariser and the analyser have the same orientation, light transmitted by the analyser has the same intensity as light transmitted by the polariser
  • i.e the intensity does not decrease between the polariser and the analyser
  • In fact, when θ = 0°, cos(0°) = 1, and I = I₀/2
• A polariser will only transmit light that is polarised parallel to its transmission axis
• This is seen in Malus’s law by the angle θ:

Table of transmission depending on polariser orientation

• The change in intensity against the angle of transmission axis is shown in the graph below

The half rule

• When unpolarised light passes through the first polariser, half the intensity of the wave is always lost ()

Brewster’s angle

• Brewster’s angle is an angle of incidence at which light with a particular polarisation is perfectly transmitted through a surface

• n₁ is the refractive index of the initial material (in this case, air)
• n₂ is the refractive index of the material scattering the light

ANSWER:   B