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Theme C — Wave Behaviour

C.3.8 Single-Slit Diffraction — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 24 of 37 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Lesson summary

C.3.8 Single-Slit Diffraction — IB PHYSICS HL notes: Describe the single-slit intensity pattern, use θ = λ/b for the first minimum and explain how slit width and wavelength change the pattern.Source — monochromatic light through a single rectangular slit of width b onto a distant…

  • Central maximum
  • Secondary maxima
  • Intensity graph
  • Longer wavelength
  • Blue light
  • White light

Part 1 of 7The single-slit pattern

Source
  • Source monochromatic light through a single rectangular slit of width b onto a distant screen
Central maximum
  • Central maximum the brightest fringe, wider than the other fringes and wider than the double-slit fringes
Secondary maxima
  • Secondary maxima much narrower and dimmer, getting dimmer with order
  • The first is only about 5% of the central intensity
Minima
  • Minima dark fringes of zero intensity from destructive interference
Intensity graph
  • Intensity graph the central peak is about twice as wide as each secondary maximum

Part 2 of 7Effect of wavelength

Longer wavelength
  • Longer wavelength the wave diffracts more so the angle of diffraction and fringe width increase
Red light
  • Red light the longest visible wavelength gives wider fringes
Blue light
  • Blue light a shorter wavelength gives narrower fringes
White light
  • White light a white central maximum with coloured side bands

Part 3 of 7Effect of slit width

Narrower slit
  • Narrower slit the angle of diffraction is greater and the waves spread out more
Intensity graph
  • Intensity graph the intensity of the maxima decreases, the central maximum widens and the fringe spacing is wider
Wide slit
  • Wide slit if b is much greater than λ the pattern shrinks towards a point with little diffraction
Slit about λ
  • Slit about λ the first minimum is near 90° and the pattern spreads across the screen
Slit width and angle
  • Slit width and angle they are inversely proportional

Part 4 of 7Single-slit geometry

Huygens principle
  • Huygens principle every point on the wavefront acts as a source of secondary coherent wavelets
Central maximum
  • Central maximum wavelets travelling straight forward (θ = 0) travel equal distances and interfere constructively
Minima
  • Minima occur where wavelets from one half of the slit cancel those from the other half
Pairing
  • Pairing each point is paired with a point b/2 away so the path difference must be λ/2
Assumption
  • Assumption the screen is much further than the slit width so the rays are nearly parallel

Part 5 of 7Position of the first minimum

1
Take a ray from the top edge and a ray from the centre of the slit.
2
Their path difference is (b/2) sin θ.
3
For destructive interference the path difference is λ/2.
4
This gives b sin θ = λ.
5
For small angles sin θ ≈ θ so θ = λ/b with θ in radians.
  • Further minima
    • θ = nλ/b for n = 1, 2, 3, …
    • At larger angles use b sin θ = nλ

Part 6 of 7Width of the central maximum

Angular width
  • Angular width from −λ/b to +λ/b, a total of 2λ/b
On a screen
  • On a screen tan θ = y/D so for small angles y = Dλ/b
Total linear width
  • 2y = 2λD/b
Increasing the width
  • Increasing the width reduce the slit width, increase the wavelength or move the screen further away

Part 7 of 7Double-slit modulation

Two interferences
  • Two interferences rays from one slit interfere with rays from the other and rays within one slit interfere with each other
Combined pattern
  • Combined pattern equally spaced double-slit fringes inside a single-slit envelope
Conditions
  • Conditions the slit width is not negligible and the slit separation is much greater than the width
Missing orders
  • Missing orders a fringe is missing where an interference maximum coincides with a diffraction minimum
Number of fringes
  • Number of fringes the ratio d/b gives the fringes inside the central peak
Resolution
  • Resolution for a circular aperture the first minimum is at θ ≈ 1.22λ/b,
    • and two sources are just resolved when the central maximum of one lies on the first minimum of the other

Key terms

TermMeaning
Central maximumThe brightest, widest band of the single-slit pattern.
Slit width (b)The width of the opening.
First minimumThe position where b sin θ = λ, giving θ = λ/b for small angles.
EnvelopeThe single-slit intensity pattern that limits a double-slit pattern.
Huygens principleEach point on a wavefront acts as a source of secondary wavelets.
Rayleigh criterionTwo images are just resolved when the peak of one lies on the first minimum of the other.

Avoid these mistakes

1
Saying a wider slit gives a wider pattern — it gives a narrower pattern.
2
Quoting λ/b as the full width of the central maximum — the full angular width is 2λ/b.
3
Confusing slit width b with slit separation d.
4
Assuming all maxima are equally bright — the central one is by far the brightest.
5
Using degrees in θ = λ/b — it needs radians.

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