What is diffraction?
A wave spreads out when it goes through a small gap or passes the edge of an object. This is called diffraction.
All waves do it: water waves, sound and light. It is clear only when the gap is about as small as the wavelength. Sound has a wavelength of about 1 metre, so it bends around doors. Light has a wavelength of about 0.0005 millimetre, so the gap must be extremely tiny.
Single slit diffraction
Shine light through one narrow slit of width a. On a screen you see a very bright wide central band and weaker bands on both sides, with dark spots between them.
The first dark spot is at angle θ where a sin θ = λ. For the n-th dark spot, a sin θ = nλ.
The central band is about twice as wide as the side bands. If you make a smaller, sin θ becomes larger, so the band gets wider.
Diffraction grating
A grating is a glass plate with thousands of very thin, equal, parallel lines. The distance between two neighbouring lines is d. If it has N lines per metre, d = 1/N.
Light from all gaps adds up. It gives bright lines where d sin θ = nλ, with n = 0, 1, 2 … (the order). The lines are thin and bright. More lines means thinner, sharper lines.
Because θ depends on λ, a grating splits white light into colours. The n = 0 line stays white. In each higher order, violet is nearest the centre and red is farthest.
Uses of diffraction
- Spectrometer: a grating splits light from a star or a lamp into its colours, so scientists can tell which elements are present.
- CDs and DVDs: the tiny tracks act as a grating and make rainbow colours.
- Limit of seeing detail: a telescope or a camera lens is a round gap. Diffraction blurs very small details.
- X-rays: the spaces between atoms in a crystal work as a grating for X-rays.
Diffraction and interference together
Interference joins waves from two or more separate sources. Diffraction is the spreading from one opening. In a real pattern both happen: each gap diffracts and the gaps interfere with each other. That is why a grating gives bright lines inside one wide, smooth envelope. See Interference of light.
Try it
Look at a CD under a lamp and tilt it. You will see colours move. Or hold two fingers close together in front of a bulb and look through the tiny gap: you see dark lines. In the 3D, predict first: if I make the gap half as wide, will the pattern become wider or narrower? Then check.
Key formulas and definitions
- Single slit, dark spots: a sin θ = nλ (n = 1, 2, 3 …)
- Grating, bright lines: d sin θ = nλ (n = 0, 1, 2 …)
- d = 1 / (lines per metre)
- Highest order: n < d / λ (because sin θ cannot be more than 1)
- Units: a, d and λ in metres (1 µm = 10⁻⁶ m, 1 nm = 10⁻⁹ m)
Worked examples
1. Light of wavelength 600 nm falls on a slit 1.2 µm wide. Find the angle of the first dark spot.
a sin θ = λ. sin θ = 600×10⁻⁹ / 1.2×10⁻⁶ = 0.5. So θ = 30°.
2. A grating has 5000 lines per cm. Find the spacing d.
5000 lines per cm = 500 000 lines per m. d = 1 / 500 000 = 2×10⁻⁶ m = 2 µm.
3. The same grating is lit with light of 500 nm. Find the angle of the first-order line.
d sin θ = λ. sin θ = 500×10⁻⁹ / 2×10⁻⁶ = 0.25. θ = about 14.5°.
4. For the same grating and 500 nm light, find the angle of the second-order line.
d sin θ = 2λ. sin θ = 2×0.25 = 0.5. θ = 30°.
5. What is the highest order seen for d = 2 µm and λ = 500 nm?
n < d/λ = 2000/500 = 4. n must be less than 4, so the highest visible order is n = 3 (at n = 4 the line would be at 90° and not seen).
6. A slit is made narrower. What happens to the central band on the screen?
a sin θ = λ, so with smaller a, sin θ gets bigger. The central band becomes wider.
Common mistakes
- Thinking light never bends. It does, but only noticeably when the gap is about one wavelength.
- Mixing up the two formulas: a sin θ = nλ gives DARK spots for a single slit; d sin θ = nλ gives BRIGHT lines for a grating.
- Forgetting to change units: lines per cm must be turned into metres before finding d.
- Saying a smaller gap makes the pattern narrower. A smaller gap makes it wider.