Single Slit Diffraction: Pattern, Formula and Width

Single slit diffraction happens when light passes through a very narrow opening and bends around its edges, spreading out instead of forming a sharp straight shadow. Each tiny part of the slit acts like a source of waves. These waves interfere with each other, making a pattern of bright and dark bands on a screen.

This effect matters because it shows light behaves as a wave. It also sets a limit on how sharply microscopes and cameras can see. If the opening is narrow, the central bright band becomes wider, and fine details get blurred.

Key Concepts

Slit width (a): The width of the single opening, measured in metres. A narrower slit gives a wider pattern.

Wavelength (λ): The wavelength of light used, in metres. Red light has a longer wavelength than blue light, so it spreads more.

Central maximum: The brightest and widest band at the centre. Its width is about twice the width of the other bright bands.

Minima: Dark points where waves from the two halves of the slit cancel exactly. Maxima occur between these minima, but get weaker away from the centre.

Formulas

Position of minima: a sin θ = n λ, where n = ±1, ±2, ±3, … . Here θ is the angle from the centre. This formula assumes a screen far away (Fraunhofer diffraction) and a slit narrow compared with the distance to the screen. It fails if a is much smaller than λ, because then sin θ would exceed 1.

Width of central maximum on screen: W = 2 λ D / a, where D is the distance from slit to screen in metres. Units: λ and a in metres, D in metres, so W comes out in metres. A larger D or λ makes the central band wider.

Worked Example

Light of wavelength 600 nm (600 × 10⁻⁹ m) passes through a slit of width 0.20 mm (2.0 × 10⁻⁴ m). The screen is 1.0 m away. Find the width of the central maximum.

Step 1: Use W = 2 λ D / a.

Step 2: Insert values: W = 2 × (600 × 10⁻⁹) × 1.0 / (2.0 × 10⁻⁴).

Step 3: Numerator = 1.2 × 10⁻⁶. Divide by 2.0 × 10⁻⁴ gives 6.0 × 10⁻³ m.

The central bright band is 6.0 mm wide. Secondary maxima are about half as wide.

Common Misconceptions

• Misconception: A narrower slit makes a narrower bright spot. Correct: A narrower slit makes the central maximum wider, because the waves spread more.
• Misconception: Diffraction and interference are the same thing. Correct: Diffraction is interference of waves from many parts of the same opening.
• Misconception: Bright bands are all equally bright. Correct: The central band is the brightest; outer bands get dimmer quickly.

Real-World Applications

Single slit diffraction is used to measure very small widths, such as a human hair, by measuring the pattern it creates. It explains why camera lenses and telescopes cannot resolve details below a certain size, and why laser beams spread slightly over long distances.

In short, when light squeezes through a narrow slit, it spreads into a bright central band with dimmer side bands. The width is set by wavelength, slit width and screen distance.