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LearnYPH11WPH12 · Unit 2: Waves and ElectricityWaves and the particle nature of lightDiffraction and interference
Waves and the particle nature of light · Subtopic 5 of 9

Diffraction and Interference

Waves spread out (diffract) through gaps about the size of their wavelength. Two coherent sources produce an interference pattern: bright fringes where the path difference is a whole number of wavelengths, dark fringes where it's a half-integer. For Young's double slits, fringe spacing x=λDax=\dfrac{\lambda D}a.

Cambridge 9702 Paper 1Cambridge 9702 Paper 2Edexcel YPH11 WPH12AQA 7408 Paper 1≈ 40 minRevision 6 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Explain diffraction and when it is significant.
  • Define coherence and state the conditions for observable interference.
  • Use path difference to predict maxima and minima.
  • Use λ=axD\lambda=\dfrac{ax}D for double-slit interference.
Pause and think

Two loudspeakers play the same note. As you walk across the room in front of them, the sound gets loud, quiet, loud, quiet. Why, when both speakers are always on?

Section 2 of 14

Core idea

Start hereLight plus light can make darkness

Shine laser light through two narrow slits and you see bright and dark stripes. At the dark places, light from one slit arrives exactly out of step with light from the other and cancels. Thomas Young used this in 1801 to prove light is a wave.

The big idea

Coherent waves: path difference nλn\lambda → maximum; (n+12)λ(n+\frac12)\lambda → minimum. Double slit: λ=axD\lambda=\frac{ax}D.

1. Path difference

Double-slit fringes: intensity on the screen
−10−55100.20.40.60.810position on screen (mm)intensitybright fringes
Bigger wavelength or bigger slit-to-screen distance DD spreads the fringes; wider slit separation aa squeezes them.
  • Constructive: 0,λ,2λ,…0,\lambda,2\lambda,\ldots
  • Destructive: 12λ,32λ,…\frac12\lambda,\frac32\lambda,\ldots
  • Needs coherent sources: constant phase difference.

2. Double slit

Path difference from two slits
S₁S₂Pbright if S₁P − S₂P = nλ
Waves leave the slits in phase. The extra distance one travels decides whether they arrive in step.
Fringe spacing x=λDax=\frac{\lambda D}a
  1. Δ=asin⁡θ\Delta=a\sin\theta
    Path difference from slits separated by aa.
  2. asin⁡θn=nλa\sin\theta_n=n\lambda
    nnth bright fringe.
  3. sin⁡θ≈tan⁡θ=ynD\sin\theta\approx\tan\theta=\frac{y_n}D
    Small angles (D≫yD\gg y).
  4. yn=nλDa⇒x=λDay_n=\frac{n\lambda D}a\Rightarrow x=\frac{\lambda D}a
    Spacing between successive fringes.
Worked exampleMeasuring λ

a=0.50a=0.50 mm, D=1.5D=1.5 m, x=1.8x=1.8 mm.

Goal
λ\lambda.
Strategy
λ=axD\lambda=\frac{ax}D in SI.
  1. λ=(0.5×10−3)(1.8×10−3)1.5\lambda=\frac{(0.5\times10^{-3})(1.8\times10^{-3})}{1.5}
    Substitute.
  2. =6.0×10−7 m=6.0\times10^{-7}\text{ m}
    600 nm: orange light.
Answer600600 nm.
✓ CheckMeasure across 10 fringes to cut the uncertainty in xx ✓.
Worked exampleMicrowaves

First minimum where path difference = 1.4 cm.

Goal
λ\lambda; path difference at the second maximum.
Strategy
First minimum is λ2\frac\lambda2.
  1. 12λ=1.4⇒λ=2.8 cm\tfrac12\lambda=1.4\Rightarrow\lambda=2.8\text{ cm}
    First minimum.
  2. 2λ=5.6 cm2\lambda=5.6\text{ cm}
    Second maximum.
Answer2.82.8 cm; 5.65.6 cm.
✓ CheckMicrowave wavelengths are cm-scale ✓.
Common misconceptionTwo separate lamps They're not coherent: no stable fringes.

Summary

  • Coherence needed.
  • λ=ax/D\lambda=ax/D.
Key words
Coherent
Constant phase difference.
Path difference
Difference in distance from the two sources.
HistoryYoung vs Newton. Newton thought light was a stream of particles. In 18011801 Thomas Young shone sunlight through two narrow slits and saw bright and dark bands: interference, which only waves can produce. British scientists were slow to accept a challenge to Newton, but Young was right.
Fun factSoap bubbles and butterflies. The colours of a soap bubble and the shimmering blue of a Morpho butterfly's wings come from interference, not pigment. Light reflecting from the top and bottom of very thin layers interferes, and different colours reinforce at different thicknesses.
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