Single-Slit Diffraction

Diffraction is the spreading of a wave as it passes through a gap or around an obstacle. It happens to all waves — water, sound, radio, light — whenever the size of the gap or obstacle is comparable to the wavelength. The single-slit diffraction pattern is a beautiful and counter-intuitive example of wave superposition in which a narrow bright central maximum is flanked by progressively dimmer secondary maxima separated by dark minima.

In the OCR A-Level Physics A specification (H556) you are not usually asked to compute the single-slit pattern quantitatively (the formula is beyond the syllabus), but you must be able to describe the pattern qualitatively, explain why it arises from superposition of waves from different parts of the slit, and contrast it with the double-slit pattern.

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Diffraction at a Single Slit

Consider a plane wave (for example, a monochromatic laser beam) hitting a narrow slit of width b, with a screen placed some distance beyond.

If the slit were infinitely narrow, every point in it would act as a single point source and the wave would spread out spherically (Huygens's principle), giving a uniformly-lit screen. Real slits, however, have a finite width, and waves from different points across the slit arrive at points on the screen having travelled slightly different distances. This path difference causes interference between the waves from different parts of the slit — and produces the characteristic single-slit diffraction pattern.

flowchart LR
    L[Monochromatic light] --> SL[Single slit of width b]
    SL --> D1[Diffraction: wave spreads out]
    D1 --> SC[Screen]
    SC --> CM[Bright central maximum: wide and intense]
    SC --> SM[Secondary maxima: much dimmer, decreasing outwards]
    SC --> Min[Dark minima in between]

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The Shape of the Pattern

The single-slit diffraction pattern has the following distinctive features:

1. A very bright, wide central maximum directly in line with the slit. This maximum is twice as wide as the other maxima and contains the overwhelming majority of the light energy.
2. A series of secondary maxima symmetrically on each side of the centre. These are much dimmer — the first secondary maximum has only about 4.5 % of the intensity of the central maximum, and the second has only about 1.6 %. Intensity drops rapidly with order.
3. Dark minima between the maxima, where the intensity is effectively zero.
4. The pattern is symmetric about the central maximum.

This is strikingly different from the double-slit pattern of Young's experiment, in which all fringes are of approximately equal intensity and equal spacing. The single-slit pattern has most of its energy in the middle.

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Why the Central Maximum Is So Wide

In the direction straight through the slit (θ = 0), all the Huygens wavelets from across the slit travel equal distances to the screen and arrive in phase. This gives a strong central maximum.

As you move slightly off-axis, the path differences across the slit remain small — the waves still mostly reinforce each other. Only when the path difference across the slit becomes exactly one wavelength does destructive interference cancel them out completely (this is the first dark minimum).

Between θ = 0 and the first minimum is the entire width of the central maximum. Beyond the first minimum, you enter the secondary maxima, but these are narrow (one wavelength's worth of path difference between adjacent minima) — only the central maximum spans from the first minimum on one side to the first minimum on the other, which is twice the width of a subsequent "bay".

The First Minimum

Although the full quantitative theory is beyond A-Level, OCR students should be aware that the first minimum of the single-slit pattern occurs at an angle given by:

b sin θ = λ

where b is the slit width. For a narrow slit (b comparable to λ), sin θ is large and the central maximum spreads widely. For a wide slit (b >> λ), sin θ is tiny and the pattern collapses to a sharp narrow spot — effectively no visible diffraction.

This explains why diffraction is everyday-obvious for sound (wavelength ~1 m, similar to typical doorways) but almost imperceptible for light (wavelength ~500 nm, far smaller than any ordinary aperture).

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Effect of Slit Width on the Pattern

Three things change as you vary the slit width b:

Slit width	Central maximum width	Secondary maxima	Pattern overall
Very narrow (b ~ λ)	Very wide	Widely spaced	Strong diffraction
Moderate (b ~ 10 λ)	Moderate	Visible	Classic pattern
Very wide (b >> λ)	Very narrow	Almost invisible	Sharp image of slit

Narrower slits give wider central maxima — the less localised the wave is as it passes through the slit, the more spread out the diffraction pattern. This is a fundamental consequence of wave behaviour and, in quantum theory, of the Heisenberg uncertainty principle applied to photons' position and momentum.

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Effect of Wavelength on the Pattern

For a fixed slit width, longer wavelengths give wider diffraction patterns: