Page plan · 20 pages

Written for: High-school physics teachers and their students

1. 1

   Waves that meet: interference and diffraction

   • Today's question: what happens when two waves occupy the same place at once?
   • Interference and diffraction are the evidence that light behaves as a wave.
   • We start with water ripples and finish with colours in soap films.
2. 2

   Lesson map: from superposition to thin films

   • Four parts: superposition, interference, diffraction, then light as a wave.
   • Each part builds on the one before it, so the order matters.
   • We finish with thin films, where all the ideas work together.
   • Practice questions and an exit ticket close the lesson.
3. 3

   Part one: superposition

   • Superposition: when waves overlap, the total displacement is the sum of the individual displacements.
   • After passing through each other, the waves continue unchanged.
   • This single principle underlies everything else in the lesson.
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   Adding two waves point by point

   • At each point, read off the displacement of each wave and add them, keeping the signs.
   • Example (illustrative): +2 cm plus +3 cm gives +5 cm; +2 cm plus -2 cm gives 0.
   • Crest meeting crest gives a larger crest; crest meeting trough cancels.
   • Try sketching two pulses and their sum on graph paper.
5. 5

   Part two: interference

   • Interference is superposition of waves that keep a steady relationship.
   • Constructive interference gives a bigger amplitude; destructive gives a smaller one.
   • The result is a fixed pattern of strong and weak regions.
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   Interference in the ripple tank

   • Two dippers in a ripple tank create two sets of circular waves.
   • Where the waves overlap, a stable pattern of lines appears.
   • Some lines show large ripples while others stay almost flat.
   • Students can see the pattern directly and trace the lines.
7. 7

   The two-source interference pattern

   • Lines of constructive interference fan out from between the two sources.
   • Between them lie lines of destructive interference, called nodal lines.
   • The pattern is symmetric about the line midway between the sources.
   • Moving the sources closer together spreads the pattern out.
8. 8

   Path difference: conditions for bright and dark

   • Path difference is the extra distance one wave travels compared with the other.
   • Bright or strong: path difference equals a whole number of wavelengths, nλ.
   • Dark or weak: path difference equals a half-integer number of wavelengths, (n + ½)λ.
   • Example (illustrative): with λ = 2 cm, a 4 cm difference is constructive.
9. 9

   Why the sources must be coherent

   • Coherent sources keep a constant phase difference over time.
   • If the phase drifts randomly, the pattern shifts and averages out to an even blur.
   • Two separate light bulbs are not coherent, so they show no fringes.
   • One source split into two beams gives a coherent pair.
10. 10

    Part three: diffraction

    • Diffraction is the spreading of waves as they pass an edge or through a gap.
    • It is a property of all waves, including water, sound and light.
    • How much spreading occurs depends on the wavelength compared with the gap.
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    Waves spreading through a gap

    • A gap about one wavelength wide produces strongly curved, spreading wavefronts.
    • A gap much wider than the wavelength gives only slight bending at the edges.
    • Narrowing the gap increases the spreading.
    • Longer wavelengths spread more through the same gap.
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    Huygens' principle: every point a new source

    • Huygens' principle: every point on a wavefront acts as a source of secondary wavelets.
    • The new wavefront is the envelope of these wavelets.
    • In a narrow gap, only a few wavelets get through, so the wave spreads out.
    • This explains both straight propagation and diffraction.
13. 13

    Part four: light as a wave

    • If light is a wave, it should show interference and diffraction.
    • The effects are small because visible wavelengths are only a few hundred nanometres.
    • We need very narrow slits and gaps to see them.
14. 14

    Young's double-slit experiment

    • Light passes through two narrow slits and falls on a distant screen.
    • Each slit acts as a coherent source because they share one incoming beam.
    • The screen shows alternating bright and dark fringes.
    • Young's result in the early 1800s supported the wave model of light.
15. 15

    A diffraction grating splits hydrogen light into lines

    • A grating splits hydrogen light into separate coloured lines by diffraction and interference.
    • Four visible Balmer lines: H-delta 4101.74 Å, H-gamma 4340.462 Å, H-beta 4861.3615 Å.
    • H-alpha is the longest at 6562.8518 Å, the red line.
    • Different wavelengths diffract to different angles, so each line appears separately.

    Column chart: Visible spectral lines of hydrogen (Balmer series). Source: Strong Lines of Hydrogen (H I), Basic Atomic Spectroscopic Data Handbook · checked 2026-10-10

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    The bright spot in the shadow of a disc

    • Light diffracts around the edge of a circular disc.
    • Waves from the rim arrive in phase at the centre of the shadow.
    • This produces a small bright spot in the middle of the shadow.
    • The spot is strong evidence for the wave model of light.
17. 17

    Colours in soap films and oil slicks

    • Light reflects from both the top and bottom surfaces of a thin film.
    • The two reflected beams interfere depending on the film thickness.
    • Thickness changes cause different colours to be reinforced.
    • Varying thickness across a soap bubble or oil slick gives swirling bands of colour.
18. 18

    Interference and diffraction on one board

    • Interference needs coherent waves overlapping, with path difference deciding the outcome.
    • Diffraction is spreading at gaps and edges, strongest when gap size is near the wavelength.
    • Young's slits, gratings and thin films combine both effects.
    • The same ideas apply to water, sound and light.
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    Practice questions on fringes and path difference

    • Practice: find the path difference for a point on the third bright fringe.
    • Practice: decide whether a half-wavelength difference gives bright or dark.
    • Practice: predict how fringes change when the wavelength increases.
    • Show your working and state the condition used.
20. 20

    Exit ticket: one wave question before you go

    • Write one answer before you leave.
    • Question: why do two separate lamps not give interference fringes?
    • Use the word coherent in your answer.
    • Bring any unanswered questions to the next lesson.