Single Slit Diffraction Calculator

Calculate diffraction minima positions and central maximum width for single slit diffraction.

1=first minimum
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Why a Single Slit Produces a Diffraction Pattern

Single-slit diffraction occurs because different parts of the same wavefront pass through the slit and interfere with one another. The central bright maximum is widest and brightest, with dark minima on either side. For a slit of width a, destructive interference occurs at angles satisfying a sinθ=mλ, where m=1,2,3,... labels the minima.

The important trend is the ratio λ/a. A longer wavelength spreads more, while a wider slit spreads less. This is why red light produces a slightly broader pattern than blue light through the same slit, and why diffraction becomes less noticeable when an opening is enormous compared with the wavelength.

a sinθ = mλ    and for small angles    y ≈ mλL/a
SymbolMeaningWhy it appears / units
aSlit widthUse meters in the formula; smaller a gives more spreading.
λWavelengthUse meters; longer wavelengths diffract more strongly.
mMinimum orderPositive integer 1, 2, 3,...; m=0 is not a minimum.
LSlit-to-screen distanceMeters; larger L spreads the pattern farther across the screen.
yDistance from center to a minimumSmall-angle result y≈L tanθ≈L sinθ.

The central maximum extends between the first minima on both sides, so its small-angle width is approximately 2λL/a. Higher-order minima exist only when mλ/a≤1 because sinθ cannot exceed 1. That condition becomes important when the slit is only a few wavelengths wide.

Worked Examples

Example 1: a=0.1mm, λ=550nm, L=2m, m=1
sinθ=550e-9/0.1e-3=0.0055
Result: y=11mm from centre
First dark fringe position
Example 2: Central max width: a=0.2mm, λ=500nm, L=3m
Width=2×500e-9×3/0.2e-3
Result: 15 mm wide
Narrower slit → wider central maximum
Example 3: Second minimum on a screen
a=0.15mm, λ=600nm, L=1.5m, m=2 → y≈mλL/a
Result: y ≈ 12 mm
The second minimum lies about twice as far from the center as the first minimum when the small-angle approximation is valid.
Example 4: A minimum that cannot exist
a=1.2µm, λ=700nm, m=2 → sinθ=mλ/a=1.17
Result: No second minimum
Because sinθ cannot exceed 1, only orders that satisfy mλ≤a are physically possible.

Common Mistakes

⚠️
Using m=0 as a dark fringe

For a single slit, m=1,2,3,... labels minima. The center m=0 is the bright central maximum, not a minimum.

⚠️
Mixing millimeters and nanometers

Convert both slit width and wavelength to consistent units before forming λ/a. Prefix errors can move the predicted fringe position by orders of magnitude.

⚠️
Using the small-angle screen formula at large angles

When θ is not small, use sinθ=mλ/a first and then y=L tanθ rather than assuming tanθ≈sinθ.

Frequently Asked Questions

Single slit vs double slit?
Single slit: minima at a sinθ=mλ (destructive). Double slit: maxima at d sinθ=mλ (constructive). In real double slit, single slit diffraction envelope modulates double slit fringes.
Why do wider slits produce narrower patterns?
Diffraction spread ∝ λ/a. Wider slit (larger a) → smaller angular spread → sharper, narrower central maximum. A very wide slit approaches geometric optics (no diffraction).
Why is the central maximum twice as wide as the others approximately?
The central maximum runs from the first minimum on one side to the first minimum on the other, giving a span of about 2λL/a. Adjacent side maxima lie roughly between successive minima separated by about λL/a, so the central bright region is approximately twice as wide.
Does changing screen distance change the diffraction angles?
No. The minimum angles are set by a sinθ=mλ, so they depend on slit width and wavelength. Increasing L does not change those angles; it increases the physical spacing y on the screen. The same angular pattern is therefore stretched over a larger distance.
What happens when the slit width becomes comparable to the wavelength?
Diffraction becomes very broad, and only a small number of minima may be possible because mλ/a must not exceed 1. The small-angle approximation can also fail. In that regime, solving for the exact angle with an inverse sine gives a more reliable result.
Why does blue light make a narrower diffraction pattern than red light?
Blue light has a shorter wavelength than red light. Since the diffraction angle scales roughly with λ/a, the shorter wavelength gives smaller minimum angles and a narrower central maximum for the same slit width and screen distance. This wavelength dependence is a direct wave effect.

Formula Explorer connections

Interpretation: This relationship connects light propagation, geometry, wavelength, refraction, interference or image formation. Assumption: Use a consistent sign convention and units. Paraxial rays, thin elements, coherent light, vacuum wavelength or ideal optical components may be assumed.

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