8.3 Interference
- Syllabus
- 9702–2028–2029
- Topic
- 8.3
- Level
- AS
Learning objectives
8.3.1The terms interference and coherence• understand the terms interference and coherence8.3.2Experiments that demonstrate two-source interference• show an understanding of experiments that demonstrate two-source interference using water waves in a ripple tank, sound, light and microwaves8.3.3The conditions required if two-source interference fringes are to be• understand the conditions required if two-source interference fringes are to be observed8.3.4Λ = ax / D for double-slit interference using light• recall and use λ = ax / D for double-slit interference using light
Path difference fixes phase difference, resultant amplitude and intensity
Interference is the variation/redistribution of resultant amplitude and intensity when waves overlap and superpose. Coherent waves have the same frequency and a constant phase difference.
phasedifferenceΔφ=2π(Δr/λ)constructive:Δr=nλ⇒Δφ=2nπdestructive:Δr=(n+1/2)λ⇒Δφ=(2n+1)π
At each point add instantaneous displacements. In-phase arrivals reinforce; antiphase arrivals oppose. For equal amplitudes the maximum amplitude doubles and a perfect minimum has zero amplitude.
I∝A2Twoequalin−phasewaves:Amax=2A0,soImax=4I0Unequalantiphasewavesleaveamplitude∣A1−A2∣,notzero.
For in-phase sources, equal path lengths give Δr=0 and a central maximum. Moving across the observation region changes the two distances and passes through alternating integer and half-integer wavelength differences.
Same frequency alone is insufficient for coherence: the phase difference must remain constant. Interference redistributes energy spatially; destructive regions do not mean energy has been destroyed.
Map two-source maxima and minima with a screen or moving detector
Create two coherent sources from one oscillator/source, keep their separation and frequency fixed, and sample the overlap region with a screen, microphone, microwave probe or ripple-tank observation.
Light: illuminate two narrow nearby slits with one monochromatic laser. Diffraction at each slit makes the beams overlap; bright/dark bands mark constructive/destructive interference. Observe safely on a screen.
Sound/microwave: drive two emitters from the same signal generator and move a detector along a line. Repeated high/low amplitude or intensity positions correspond to integer/half-integer wavelength path differences.
Ripple tank: two in-phase dippers produce antinodal lines where crest meets crest/trough meets trough and nodal lines where crest meets trough. Use a strobe to make the pattern easier to see.
Mark several successive maxima/minima, measure across multiple intervals and divide by the number of gaps. Identify the central maximum from equal paths before assigning order.
The bands or nodal lines are positions of repeated superposition, not barriers or permanent wave tracks. A reflected single-source pattern may interfere too, but it is not the same two-source geometry.
Separate the conditions for stable, visible and well-spaced fringes
Stable positions require coherent sources: same frequency and constant phase difference. Splitting one source with two slits provides coherence; two independent lamps have rapidly changing relative phase and wash out fringes.
Both waves must reach each observation point. Narrow slits provide diffraction and overlap; suitable slit separation and a sufficiently distant screen produce resolvable path-difference changes.
Comparable arriving amplitudes give high visibility: bright maxima are strong and dark minima can approach zero. Reducing one slit intensity makes maxima dimmer and minima brighter, so contrast decreases.
fringespacingx=λD/aChangingamplitudedoesnotchangex.LargerλorDincreasesx;largerslitseparationadecreasesx.
A narrow wavelength range prevents different fringe spacings from overlapping. Mechanical/thermal stability preserves path difference during observation; align screen/detector so the intended geometry is measured.
Coherence controls stability, amplitude balance controls contrast, and λ/a/D controls spacing. Do not use one of these to explain an effect governed by another.
Double-slit fringe spacing follows λ=ax/D for small angles
For slit separation a and screen distance D, the fringe spacing x satisfies λ=ax/D in the small-angle approximation.
Use consistent units and identify x as adjacent bright-fringe spacing, not distance from the centre unless the count is included.
With a=0.25 mm, D=2.0 m and x=5.0 mm, λ=6.25×10⁻⁷ m.
Increasing slit separation reduces fringe spacing; increasing screen distance or wavelength increases it.