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Interference and Diffraction
Waves & Optics
When waves meet, they add up. Where they arrive in step they reinforce each other, and where they arrive out of step they cancel — and when a wave passes a small opening, it spreads out.
Interference
Interference is what happens when two or more waves overlap. By the principle of superposition, the total displacement at any point is the sum of the displacements of the individual waves. If the waves arrive in phase, crest on crest, they add to make a larger wave: constructive interference. If they arrive in antiphase, crest on trough, they cancel: destructive interference. For light, constructive interference gives a bright fringe and destructive interference a dark fringe. Interference is only stable and easy to see when the sources are coherent, meaning they keep a constant phase relationship, as the two slits in Young's experiment do.
Diffraction
Diffraction is the spreading of a wave as it passes through a gap or around an edge. It is most noticeable when the gap or obstacle is about the same size as the wavelength. A wide doorway lets sound spread into the next room, while a narrow slit makes a beam of light spread into a pattern of bright and dark fringes. The single-slit pattern has a wide, bright central maximum and fainter maxima on either side. Diffraction sets a fundamental limit on resolution: no telescope or microscope can resolve details much smaller than the wavelength of the light it uses, however good its lenses are.
Where you see it
Young's double-slit experiment produced the first clear proof that light behaves as a wave, and the same pattern appears for electrons, showing that matter waves interfere too. Diffraction gratings, with thousands of closely spaced slits, split light into spectra and are used in spectrometers to identify chemicals by their spectral lines. The colours on a CD or a soap film come from interference between light reflected from different surfaces. Radio telescopes use interference between widely separated dishes to achieve the resolution of a single enormous telescope.
📝 Worked example: double-slit fringe spacing
In a double-slit experiment, light of wavelength lambda = 600 nm passes through slits separated by d = 0.20 mm. The screen is L = 2.0 m away. Use fringe spacing delta x = lambda L / d. Convert: lambda = 600 x 10^-9 m = 6.0 x 10^-7 m, d = 0.20 x 10^-3 m = 2.0 x 10^-4 m. Substitute: delta x = (6.0 x 10^-7) x 2.0 / (2.0 x 10^-4). Numerator: 1.2 x 10^-6. Divide by 2.0 x 10^-4 gives 6.0 x 10^-3 m. The fringes are 6.0 mm apart.
Common mistakes
- Thinking interference destroys energy: energy is redistributed, with bright and dark regions, and the total energy is conserved.
- Confusing diffraction with refraction: diffraction is spreading around an edge or through a gap; refraction is bending when speed changes.
- Expecting a sharp shadow from a narrow slit: the narrower the slit, the more the light spreads, which is the opposite of the ray picture.
Practice questions
- Light of 500 nm passes through slits 0.10 mm apart onto a screen 1.5 m away. What is the fringe spacing?
Show answer
delta x = (5.0 x 10^-7) x 1.5 / (1.0 x 10^-4) = 7.5 x 10^-7 / 1.0 x 10^-4 = 7.5 x 10^-3 m = 7.5 mm.
- What happens to a single-slit pattern if the slit is made narrower?
Show answer
The central maximum becomes wider, because the first minimum moves to a larger angle.
- When do two waves interfere constructively?
Show answer
Constructive interference at a path difference of one whole wavelength, or any whole number of wavelengths.
Frequently asked questions
What are the two types of interference?
Constructive interference, where waves arrive in phase and add up; destructive interference, where they arrive in antiphase and cancel.
Can you hear sound around a corner?
Yes, that is diffraction: sound bends around corners and through doorways, which is why you can hear someone in the next room.