Polarisation

AS Level Physics · Waves. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.

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The idea

In an unpolarised transverse wave the vibrations are in many directions, all at right angles to the direction of travel. In a plane-polarised wave the vibrations are in one direction only. Polarisation is possible only for transverse waves. Longitudinal waves such as sound vibrate along the direction of travel, so there is nothing to select.

A polarising filter lets through only the part of the vibration that lies along its transmission axis. If plane-polarised light meets a filter whose axis is at angle θ to its plane of polarisation, the amplitude that gets through is A0 cos θ. Intensity depends on amplitude squared, which gives Malus's law. The light leaving is polarised along the axis of that filter.

Rules to remember

Common mistake

Students forget to square the cosine, or with two filters they measure the second angle from the original light. After the first filter the light is polarised along that filter's axis, so measure the next angle from there.

Worked example

Plane-polarised light of intensity 60 W m−2 passes through two polarising filters. The first has its axis at 45° to the plane of polarisation. The second has its axis at 90° to the original plane of polarisation. What is the final intensity? (cos 45° = 0.707)

  1. After the first filter: I1 = 60 × cos245° = 60 × 0.50 = 30 W m−2
  2. This light is now polarised along the first axis, so its angle to the second axis is 90° − 45° = 45°
  3. After the second filter: I2 = 30 × cos245° = 30 × 0.50 = 15 W m−2

Answer: 15 W m−2

Practice questions

Try each one, then open the answer.

1. Plane-polarised light passes through a polarising filter and half of its intensity is transmitted. What is the angle between the transmission axis and the plane of polarisation?

  1. A
    30°
  2. B
    45°
  3. C
    60°
  4. D
    90°
Show answer

Answer: B. cos2θ = 0.50, so cos θ = 0.707 and θ = 45°. At 60° only a quarter would be transmitted.

2. Plane-polarised light of intensity 80 W m−2 passes through two polarising filters. The first has its axis at 30° to the plane of polarisation; the second has its axis at 90° to the plane of polarisation. What is the final intensity? (cos 30° = 0.866, cos 60° = 0.500)

  1. A
    0
  2. B
    15 W m−2
  3. C
    20 W m−2
  4. D
    60 W m−2
Show answer

Answer: B. After the first filter: 80 × cos2 30° = 60 W m−2. The second filter is at 60° to the first: 60 × cos2 60° = 15 W m−2. The middle filter stops the result being zero.

3. Which observation shows that light is a transverse wave?

  1. A
    light can be polarised
  2. B
    light can be refracted
  3. C
    light can be diffracted
  4. D
    light shows interference
Show answer

Answer: A. Only transverse waves can be polarised. Diffraction, refraction and interference happen with longitudinal waves such as sound too.

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