Single-Slit Diffraction Simulator — Wave Optics Visualized

simulator intermediate ~8 min
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Central max width: 0.55 mm — A 2 μm slit diffracts 550 nm light into a broad central maximum with visible side lobes.

A 2 micrometer slit illuminated with 550 nm green light produces a central diffraction maximum 0.55 mm wide at 1 meter distance, with diminishing side lobes.

Formula

I(θ) = I₀ × (sin(β)/β)²  where β = πa sin(θ)/λ
minima: a sin(θ) = mλ  (m = ±1, ±2, ...)
θ_Rayleigh = 1.22 λ/D

Light Bends Around Corners

When light passes through a narrow slit, it doesn't simply project a sharp shadow of the slit onto a distant screen. Instead, it spreads out, creating a broad central bright band flanked by alternating dark and bright fringes. This is diffraction — direct evidence that light behaves as a wave. The effect becomes dramatic when the slit width approaches the wavelength of light. If slits were infinitely narrow, light would spread in all directions equally. The finite slit width creates the characteristic sinc-squared intensity pattern.

The Single-Slit Pattern

The intensity distribution from a single slit follows I(θ) = I₀(sin β/β)², where β = πa sin(θ)/λ. The central maximum is twice as wide as each side lobe and contains about 84% of the total transmitted light energy. Dark fringes (minima) occur where a sin(θ) = mλ for integer m, corresponding to positions where light from different parts of the slit destructively interferes. The narrower the slit, the broader the pattern — a direct manifestation of Heisenberg's uncertainty principle applied to photon position and momentum.

Resolution and the Diffraction Limit

Diffraction sets a fundamental limit on the resolution of all optical instruments. A circular aperture of diameter D cannot resolve two point sources closer than θ = 1.22λ/D — the Rayleigh criterion. This is why radio telescopes (long wavelengths) must be enormous to achieve useful resolution, while electron microscopes (extremely short de Broglie wavelength) can resolve individual atoms. The diffraction limit is not a technology problem to be solved but a fundamental consequence of wave physics.

Beyond the Single Slit

Single-slit diffraction is the building block for understanding more complex optical phenomena. Double-slit interference (Young's experiment) combines diffraction with two-source interference to produce the iconic fringe pattern. Diffraction gratings — arrays of thousands of slits — produce extremely sharp spectral lines used to analyze starlight and characterize materials. Even the Fourier transform has a direct physical analog in Fraunhofer diffraction: the far-field diffraction pattern is the Fourier transform of the aperture function.

FAQ

What is diffraction?

Diffraction is the spreading of waves as they pass through an aperture or around an obstacle. It occurs when the aperture size is comparable to the wavelength. For visible light, apertures of a few micrometers produce easily observable diffraction patterns.

Why does a narrower slit produce a wider diffraction pattern?

This counter-intuitive result follows from the uncertainty principle: confining a wave to a smaller region (narrow slit) increases the spread of its momentum directions. Mathematically, the angular width of the central maximum is 2λ/a — inversely proportional to slit width a.

How does diffraction limit telescope resolution?

Even a perfect lens acts as a circular aperture, producing an Airy diffraction pattern. The angular resolution limit is θ = 1.22λ/D, where D is the aperture diameter. This is why larger telescopes (and shorter wavelengths) give sharper images.

What is the difference between diffraction and refraction?

Refraction is the bending of light due to a change in speed between media (Snell's Law). Diffraction is the spreading of light as it passes through or around obstacles, caused by the wave nature of light. Both alter light's direction but through fundamentally different mechanisms.

Sources

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