Diffraction of Light
Simple Explanation
Diffraction is the spreading of light as it passes through a narrow opening (or around an obstacle) — a single narrow slit produces its own pattern of bright and dark bands, with dark bands (minima) at angles given by a sinθ=mλ.
Why Do We Need It?
Diffraction sets a fundamental limit on the sharpness of images formed by any lens or telescope — no optical instrument, however perfectly made, can beat the blurring diffraction causes.
See It
A graph showing a tall central peak at the center, flanked by much smaller side peaks that decrease in height further from the center, with the intensity dropping to zero between each peak
Formula
Single-Slit Diffraction Minima
a sinθ = mλ
Light passing through a single narrow slit spreads out and produces a pattern of dark bands (minima) at specific angles, determined by the slit's width relative to the light's wavelength.
- a
- — width of the slit, in metres (m)
- θ
- — angle from the center to the dark band, in degrees
- m
- — order of the minimum (m=1, 2, 3, …, not m=0)
- λ
- — wavelength of the light, in metres (m)
When to use it: Whenever the angle of a dark band in a single-slit diffraction pattern needs to be found (or the slit width worked out from a known dark-band angle).
Worked Example
Find the angle of the first diffraction minimum
Light of wavelength 500 nm passes through a single slit 0.2 mm wide. Find the angle of the first diffraction minimum (m=1).
Why Does This Work?
Using Huygens' principle, every point across the open slit acts as a wavelet source — at the first minimum angle, wavelets from the top half of the slit exactly cancel wavelets from the bottom half in pairs (each pair differing by half a wavelength in path length), producing complete destructive interference at that specific angle.
Real-Life Example
Why telescope images have a fundamental sharpness limit
Even a perfectly-made telescope lens cannot produce an infinitely sharp point of light from a distant star — instead it shows a small blurred disk.
This blur comes directly from diffraction at the telescope's circular aperture (opening) — a fundamental physical limit that no amount of manufacturing precision can eliminate, only reduce by using a larger aperture.
Practice
Light of wavelength 600 nm passes through a single slit 0.1 mm wide. Find the angle of the first minimum, in degrees.
HardCommon mistake
Confusing single-slit diffraction minima (a sinθ=mλ) with double-slit interference maxima (Δy=λL/d) — they describe different patterns from different setups, and mixing up their formulas gives a nonsensical answer.
Quick Review
- a sinθ = mλ — dark bands (minima) from a single slit.
- Caused by wavelets from different parts of the slit canceling each other.
- Sets a fundamental resolution limit for any optical instrument.