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17.2Interference and Diffraction

Diffraction — American System Physics Revision Notes & Topical Questions

10 min read 7 parts Lesson 4 of 5 1 quiz

📚 American System Physics Hub / Topical Revision
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Lesson summary

Describe diffraction of waves at a gap and at an edge.Single slit, first dark minimaw sin θ = λ (for small angles θ ≈ λ/w, θ in radians).Single-slit dark fringesw sin θ = mλ, m = 1, 2, 3 …Width of central maximum on a screen at distance L: 2x1 = 2λL/w (m).Rayleigh criterion, circ…

  • Wave equation still applies
  • Huygens' principle explains diffraction
  • For the slit above, a screen is 2.0 m away. How wide is the central maximum?
  • Aperture (gap width, w)
  • Single-slit diffraction pattern
  • Diffraction condition for large effect

Section 1 of 7Diffraction

Essential knowledge
17.2 Diffraction concept map: Single slit, first dark minima, Single-slit dark fringes, Wave equation still applies, Huygens' principle explains d, For the slit above, a screen
Visual guide to the key ideas explained in this lesson.
All waves diffract. When plane wavefronts meet a gap, the part of the wave passing through spreads out into the region behind the barrier; the wavefront spacing (wavelength) remains the same.
The amount of spreading depends on the ratio of wavelength to gap width: the closer the gap is to λ, the more the wave spreads.
Huygens' principle explains diffraction
Huygens' principle explains diffraction each point in the gap acts as a new source of wavelets, so the wave can spread out sideways.
Long-wave radio signals (λ of hundreds of metres) diffract around hills and buildings, so reception is good in valleys; short-wave TV and mobile signals diffract less and need line-of-sight transmitters.
We hear people round corners but cannot see them because sound wavelengths are comparable with doorway widths, while light wavelengths are about a million times smaller.
In a single-slit pattern, wavelets from different parts of the slit interfere. At angle θ where w sin θ = λ, wavelets from the top half cancel those from the bottom half, giving the first dark band.
Narrowing the slit makes the central maximum wider (and dimmer); using longer-wavelength light also widens it.
Double-slit fringes are really an interference pattern inside a single-slit diffraction envelope, because each slit also diffracts.
Because each point source produces a small diffraction disc, a telescope with a larger aperture D or shorter wavelength resolves finer detail. This is one reason big mirrors are built and why electron microscopes (very short wavelength) resolve more detail than light microscopes.
Diffraction around an edge produces faint fringes at the edge of shadows, so shadows are never perfectly sharp.

Section 2 of 7Process & sequence

1
Fill a ripple tank with water to a uniform depth of about 1 cm and switch on the lamp and a plane-wave dipper.
2
Place two metal barriers in the water to make a gap much wider than the wavelength; observe the wavefronts on the screen.
3
Gradually move the barriers closer until the gap is about the same as the wavelength.
4
Observe that the diffracted wavefronts become more curved and spread further into the shadow region.
5
Keep the gap fixed and increase the dipper frequency (shorter λ); observe less spreading.
6
Record observations with sketches or photographs, noting that the wavelength (spacing of wavefronts) is the same before and after the gap.

Plane waves passing through a gapwrite these steps in this order; each step is a marking point.

1
Straight, equally spaced wavefronts approach the barrier.
2
Only the part of each wavefront level with the gap passes through.
3
Each point in the gap sends out circular wavelets.
4
The wavelets combine into curved wavefronts spreading into the shadow region.
5
Wavefront spacing (wavelength) is unchanged; spreading is greatest when the gap ≈ λ.

Section 3 of 7Compare

How gap width affects diffraction (wavelength fixed)
Gap width compared with λAmount of spreadingExample
Much larger than λVery little; mainly straight-through beam with slight edge bendingLight through a doorway
Similar to λLarge; wavefronts become nearly semicircularSound through a doorway (λ ≈ 1 m)
Smaller than λWave spreads strongly but little energy gets throughMicrowaves and a mesh screen

Longer wavelength with the same gap gives more spreading: that is why you can hear round corners but not see round them.

Diffraction versus refraction versus interference
EffectCauseChanges
DiffractionWave passes gap/edgeDirection spreads; λ, v, f unchanged
RefractionWave enters new mediumSpeed and λ change; f unchanged
InterferenceTwo coherent waves overlapAmplitude pattern (maxima/minima)

Section 4 of 7Worked examples

Worked examples
0.29°
Light of wavelength 600 nm passes through a slit 0.12 mm wide. Find the angle to the first dark minimum.
  • sin θ = λ/w = 600 × 10−9 / 0.12 × 10−3 = 5.0 × 10−3, so θ = 0.29° (5.0 × 10−3 rad).
For the slit above, a screen is 2.0 m away. How wide is the central maximum?
  • Distance to first minimum x1 = λL/w = 600 × 10−9 × 2.0 / 0.12 × 10−3 = 1.0 × 10−2 m.
    • Width = 2x1 = 2.0 × 10−2 m (2.0 cm).
A telescope has an aperture of diameter 0.10 m. Find the smallest angle it can resolve for light of wavelength 550 nm.
  • θ = 1.22λ/D = 1.22 × 550 × 10−9 / 0.10 = 6.7 × 10−6 rad.

Section 5 of 7Key terms

Section 6 of 7Command terms

Command terms
Identify / Describe (FRQ)
A short, specific statement; describing requires relevant characteristics, not a single word.
Explain / Justify (FRQ)
Give the cause-and-effect reasoning or evidence; a restated fact does not score.
Calculate
Show setup, substitution and the answer with units.
Predict
State the expected outcome; add a reason only if asked to justify.
MCQ technique
Read every option; eliminate distractors that are true statements but do not answer the question; watch for NOT/EXCEPT.

Section 7 of 7Exam technique

Keywords the mark scheme looks for in this lesson

Keywords the mark scheme looks for in this lesson
Diffraction · Aperture (gap width, w) · Wavefront · Huygens' principle · Single-slit diffraction pattern · Central maximum · Diffraction condition for large effect · Resolution · Rayleigh criterion · Ripple tank
Learn each definition in the Key words tab exactly; a missing keyword in a definition usually loses the mark.

How to get full marks (examiner guidance)

1
Answer exactly what is asked; extra correct material does not earn credit, and contradictory statements can cancel credit (AP FRQ).
2
Use precise vocabulary, never “it/stuff/things”.
3
Show units and working in calculations.
4
In MCQs, predict the answer before reading the options, then eliminate.

Words to avoid

1
the wavelength gets bigger after the gapthe wavelength stays the same; only the direction of travel spreads.
2
diffraction is waves bendingdiffraction is the spreading of waves as they pass through a gap or around an edge.
3
more diffraction with a bigger gapmore diffraction when the gap is narrower, closest to the wavelength.
4
diffraction happens because the wave slows downrefraction involves speed change; diffraction occurs without any change in speed.
5
all bright bands in single-slit diffraction are equalthe central maximum is twice as wide and much brighter than the side maxima.

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