Single-Slit Diffraction

Core Idea

When light passes through a single finite-width slit, it diffracts and produces a pattern with a wide bright central maximum flanked by narrower secondary maxima. Dark fringes (minima) occur at angles where asinθ = mλ (m = ±1, ±2, …), where a is the slit width. Narrower slits produce wider central maxima — an inverse relationship between slit width and diffraction spreading that fundamentally limits optical resolution.

How It's Best Learned

Shine a laser through progressively narrower slits and observe the central maximum widening. Compare single-slit and double-slit patterns to understand how single-slit diffraction modulates the double-slit fringe envelope.

Common Misconceptions

• Diffraction minima for a single slit are at integer multiples of λ/a (unlike double-slit maxima), leading to sign/condition confusion.
• Diffraction occurs for any wave passing any opening; it becomes visible when aperture size is comparable to wavelength.

Explainer

From your work on wave interference, you know that two coherent waves can add constructively (crest meets crest) or destructively (crest meets trough). In double-slit diffraction, you treated each slit as a point source. Single-slit diffraction asks: what happens when the slit has a finite width and cannot be treated as a point? The answer comes from Huygens's principle: every point across the width of the slit acts as an independent point source of secondary wavelets. The single slit is not one source — it is many sources spread across the aperture, all interfering with each other at the screen.

To find the dark fringes, divide the slit of width a into pairs of sources separated by half the slit width. At a specific angle θ, the path difference between the top of the slit and the point a/2 below it is (a/2)sinθ. When that path difference equals λ/2, those two sources cancel. But if those two cancel, you can pair up every source in the top half with one in the bottom half — the entire slit cancels, producing the first dark fringe. This occurs when (a/2)sinθ = λ/2, or equivalently asinθ = λ. Repeating the argument by dividing the slit into 4, 6, 8... equal parts gives the general condition for minima: asinθ = mλ for m = ±1, ±2, ….

The inverse relationship between slit width and diffraction spread is the most important takeaway. A narrow slit (a small) requires a smaller θ for path differences to reach λ — so the first minimum appears far from center, and the central maximum is wide. A wide slit has many sources that quickly cancel at small angles — the central maximum is narrow. In the limit of a very wide slit, diffraction spreading becomes negligible and you get a sharp geometric shadow. This trade-off — wide aperture gives sharp edges but poor resolving power for closely spaced features, narrow aperture gives broad diffraction but finer angular sensitivity — is fundamental to telescope and microscope design.

Comparing single-slit to double-slit patterns is illuminating. Double-slit produces equally spaced bright fringes. Single-slit produces a bright central maximum that is twice as wide as the secondary maxima, flanked by progressively dimmer bands. When you have both a double slit and finite slit width — the realistic case — the double-slit interference fringes are modulated by the single-slit envelope. Some double-slit maxima are suppressed entirely wherever they coincide with a single-slit minimum. Recognizing this modulation is what separates real optical analysis from idealized point-source models.