Interference

AS Level Physics · Superposition. 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

When two waves meet, their displacements add. Interference is the pattern this produces. Where the waves always arrive in phase they give a large amplitude (constructive). Where they always arrive in antiphase they cancel (destructive).

The pattern stays still only if the sources are coherent: they keep a constant phase difference, which needs the same frequency. Two separate lamps are not coherent, so light from one source is sent through two slits. Two loudspeakers on one signal generator, two dippers on one bar in a ripple tank, or microwaves through two gaps do the same job.

What you observe at a point depends on the path difference from the two sources to that point.

Rules to remember

Common mistake

Students forget to convert units and to find one fringe spacing. Change mm and nm to metres first, and if a length covers ten fringe spacings, divide it by ten to get x.

Worked example

Light of wavelength 500 nm passes through two slits 0.25 mm apart. The screen is 1.2 m from the slits. What is the fringe spacing?

  1. Convert: λ = 5.0 × 10−7 m, a = 2.5 × 10−4 m, D = 1.2 m.
  2. Rearrange λ = ax/D to give x = λD/a.
  3. x = (5.0 × 10−7 × 1.2) ÷ (2.5 × 10−4) = 6.0 × 10−7 ÷ 2.5 × 10−4 = 2.4 × 10−3 m.

Answer: The fringe spacing is 2.4 mm.

Practice questions

Try each one, then open the answer.

1. Two waves meet at a point with a phase difference of 180° and equal amplitudes. What is observed?

  1. A
    constructive interference, doubled amplitude
  2. B
    destructive interference, zero amplitude
  3. C
    no interference
  4. D
    a stationary wave
Show answer

Answer: B. Antiphase waves of equal amplitude cancel: destructive interference. In phase they add to double the amplitude.

2. In a double-slit experiment, which change increases the fringe spacing?

  1. A
    moving the screen closer to the slits
  2. B
    using light of shorter wavelength
  3. C
    moving the slits closer together
  4. D
    making the slits narrower
Show answer

Answer: C. x = λD/a: smaller slit separation a, longer wavelength, or larger distance D all increase the spacing.

3. Two coherent waves of amplitudes 3.0 mm and 1.0 mm arrive at a point in antiphase. What is the amplitude of the resultant oscillation?

  1. A
    0
  2. B
    1.0 mm
  3. C
    2.0 mm
  4. D
    4.0 mm
Show answer

Answer: C. In antiphase the displacements are always opposite, so the resultant amplitude is 3.0 − 1.0 = 2.0 mm. Complete cancellation needs equal amplitudes.

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