⎸ Slit diffraction
A wave passes through a single slit: field and screen simulation, comparison with sinc², single photons and a calculator for minima.
Slit width a40 px
Wavelength λ12 px
View:
Mode:
Examples:
What the screen shows
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First minimum angle θ₁
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Central maximum width ≈ 2λL/a
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Minima on the screen
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Diffraction regime
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Photons on the screen
Minima: a·sin θ = m·λ, m = ±1, ±2, …
Intensity: I(θ) = I₀ · sinc²(π a sin θ / λ)
Central maximum width: ≈ 2·λ·L / a
Intensity: I(θ) = I₀ · sinc²(π a sin θ / λ)
Central maximum width: ≈ 2·λ·L / a
- The “Rays” view is a simplified geometric diagram: the source, rays through the slit and a fan of rays to the screen. It is an illustration, not particle trajectories. The “Wave field” view shows the real sum of waves: the slit is divided into dozens of point sources following Huygens’ principle.
- Narrow the slit and the central spot on the screen widens. When a ≤ λ, the wave spreads out as a semicircle and there are no minima at all.
- On the right are the screen and the I(y) graph. The solid line is the calculation for a screen at a finite distance; the yellow dashed line is the ideal far-field sinc² curve. The wider the slit, the more they differ (near field).
- In the “Single photons” mode each particle lands on the screen at random, and the central maximum and side maxima emerge only after many hits.
- The colour corresponds to the wavelength; pixels in the simulation are arbitrary (λ from 8 to 30 px ≈ 400–700 nm).
Enter real parameters: wavelength, slit width and distance to the screen. You get the positions of the minima, the width of the central spot and the Fresnel number.
Wavelength λ, nm
Slit width a, mm
Distance to screen L, m
Minimum order m
Examples:
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Angle θm of the mth minimum, °
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Position of the mth minimum from the centre, mm
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Central maximum width, mm
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First side maximum from the centre, mm
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Highest minimum order m
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Fresnel number NF = (a/2)² / λL
Minimum m: sin θm = m·λ / a, ym = L · tan θm
First side maximum: sin θ ≈ 1.43·λ / a, intensity ≈ 4.7 % of the central one
Far field (Fraunhofer): NF ≪ 1
First side maximum: sin θ ≈ 1.43·λ / a, intensity ≈ 4.7 % of the central one
Far field (Fraunhofer): NF ≪ 1
Slit width and the pattern on the screen (λ = 650 nm, L = 2 m)
| a, mm | θ₁, ° | Central max. width, mm | Comment |
|---|---|---|---|
| 0.02 | 1.86 | 130.07 | Very narrow slit: the pattern is spread over tens of centimetres |
| 0.05 | 0.74 | 52 | Typical slit for a lab experiment |
| 0.1 | 0.37 | 26 | 3–5 side maxima clearly visible |
| 0.2 | 0.19 | 13 | The central spot shrinks |
| 0.5 | 0.07 | 5.2 | Diffraction barely noticeable |
| 1 | 0.04 | 2.6 | Almost a geometric shadow |
Single-Slit Diffraction Online: Simulation and Calculator
A free interactive tool that shows how a wave spreads out behind a narrow slit. Change the slit width and wavelength and watch the wave field behind the barrier, the pattern on the screen and the intensity graph compared with the ideal sinc² curve. The “Single photons” mode reproduces how the pattern builds up from individual hits. The calculator works out the minima, the width of the central spot and the Fresnel number for real lasers.
Key concepts
Diffraction
The bending of waves around obstacles and their spreading behind openings. It is noticeable when the size of the opening is comparable to the wavelength or smaller.
a ≈ λ → the wave spreads out as a semicircle
Intensity minima
Directions in which secondary waves from different parts of the slit cancel each other. The central maximum is twice as wide as the side ones.
a·sin θ = m·λ
Fresnel number
Shows whether the screen is in the far field. For NF ≪ 1 the simple Fraunhofer pattern applies; for NF ≳ 1 it is the Fresnel near field with a different shape.
NF = (a/2)² / λL
Where it is used
- Wave optics lab work: measuring the slit width or the wavelength
- Resolving power of telescopes, microscopes and cameras (the diffraction limit)
- Measuring the thickness of a hair or thread from its diffraction pattern
- Acoustics: why sound can be heard around the corner of a building
- X-ray and electron diffraction by crystals
- Design of antennas and radio telescopes
How to use
- Move the slit width slider a: the central maximum on the screen widens or narrows
- Change the wavelength λ: the colour and the width of the pattern change together
- Find the regime a ≈ λ, where there are no minima and the wave spreads out as a semicircle
- Compare the calculation with the dashed sinc² curve on the graph
- Switch to “Single photons” and watch the pattern emerge from dots
- In the “Calculator” tab enter your own λ, a and L
Frequently asked questions
What is single-slit diffraction?
It is the spreading of a wave behind a narrow opening: instead of a straight beam, the wave fans out sideways, and the screen shows a wide central maximum and weaker side maxima separated by dark minima. The narrower the slit relative to the wavelength, the more noticeable the diffraction.
Why do dark fringes appear on the screen?
By Huygens’ principle every point of the slit emits a secondary wave. At an angle θ where sin θ = mλ/a (m = 1, 2, 3…), the slit can be divided into pairs of points whose waves cancel each other. Intensity minima appear in these directions.
Why does a narrower slit give a wider pattern?
The angle of the first minimum is given by sin θ₁ = λ/a, so the smaller the slit width a, the larger the angle and the wider the central maximum. The width of the central spot on a screen at distance L is approximately 2λL/a.
How does single-slit diffraction differ from Young’s experiment?
In Young’s experiment two slits produce dense interference fringes, and the diffraction at each slit sets their envelope: I = I₀ · cos²(πd sin θ/λ) · sinc²(πa sin θ/λ). A single slit gives only the envelope, without the fine fringes.
Why does sound bend around corners, but light does not?
Diffraction is noticeable when the width of the opening or obstacle is comparable to the wavelength or smaller. The wavelength of sound in air ranges from centimetres to metres, comparable to a doorway, so sound is easily heard around a corner. The wavelength of visible light is less than a micrometre, so diffraction is unnoticeable for ordinary objects.