Learn9702Paper 2 · AS Level Structured QuestionsSuperpositionDiffraction and interference

Superposition · Subtopic 2 of 3

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 $x=\dfrac{\lambda D}a$ .

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 $\lambda=\dfrac{ax}D$ 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 $n\lambda$ → maximum; $(n+\frac12)\lambda$ → minimum. Double slit: $\lambda=\frac{ax}D$ .

1. Path difference

Double-slit fringes: intensity on the screen

fringe spacing x (mm) = 1.5

Bigger wavelength or bigger slit-to-screen distance

D

spreads the fringes; wider slit separation

a

squeezes them.

Constructive: $0,\lambda,2\lambda,\ldots$
Destructive: $\frac12\lambda,\frac32\lambda,\ldots$
Needs coherent sources: constant phase difference.

2. Double slit

Path difference from two slits

Waves leave the slits in phase. The extra distance one travels decides whether they arrive in step.

Fringe spacing

x=\frac{\lambda D}a

$\Delta=a\sin\theta$
Path difference from slits separated by $a$ .
$a\sin\theta_n=n\lambda$
$n$ th bright fringe.
$\sin\theta\approx\tan\theta=\frac{y_n}D$
Small angles ( $D\gg y$ ).
$y_n=\frac{n\lambda D}a\Rightarrow x=\frac{\lambda D}a$
Spacing between successive fringes.

Worked exampleMeasuring λ

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

Goal: $\lambda$ .
Strategy: $\lambda=\frac{ax}D$ in SI.

$\lambda=\frac{(0.5\times10^{-3})(1.8\times10^{-3})}{1.5}$
Substitute.
$=6.0\times10^{-7}\text{ m}$
600 nm: orange light.

Answer

600

nm.

✓ CheckMeasure across 10 fringes to cut the uncertainty in

x

✓.

Worked exampleMicrowaves

First minimum where path difference = 1.4 cm.

Goal: $\lambda$ ; path difference at the second maximum.
Strategy: First minimum is $\frac\lambda2$ .

$\tfrac12\lambda=1.4\Rightarrow\lambda=2.8\text{ cm}$
First minimum.
$2\lambda=5.6\text{ cm}$
Second maximum.

Answer

2.8

cm;

5.6

cm.

✓ CheckMicrowave wavelengths are cm-scale ✓.

Common misconceptionTwo separate lamps They're not coherent: no stable fringes.

Summary

Coherence needed.
$\lambda=ax/D$ .

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

1801

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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