How Double-Slit Interference Works and Why It Matters

If you shine light through two narrow, closely spaced slits onto a screen, you do not see two bright bands. You see a row of many evenly spaced bright and dark stripes. This pattern, called an interference pattern, is one of the clearest proofs that light behaves as a wave. Thomas Young demonstrated it in the early 1800s, and the same experiment, repeated with electrons, became one of the central puzzles of quantum physics.

This post explains where the stripes come from, how to calculate where they appear, and why the result matters beyond optics.

Waves add together

Every wave, whether it is sound, water or light, can be described by its amplitude, which is the height of the wave at a given point. When two waves meet at the same place, their amplitudes add. This principle is called superposition.

If two peaks arrive at the same point together, they reinforce each other and the amplitude doubles. If a peak meets a trough of equal size, the two cancel and the amplitude is zero. Interference is simply this addition of waves, with peaks and troughs either lining up or cancelling.

Setting up the experiment

Imagine a plane wave of monochromatic light, meaning one wavelength, hitting a barrier with two narrow slits. Each slit acts as a new source of circular waves, following the Huygens principle. The two sets of circular waves spread out and overlap on a distant screen.

At most points on the screen, the two waves arrive with different path lengths. The difference in distance travelled from each slit to a point on the screen is called the path difference. When the path difference equals a whole number of wavelengths, the peaks line up and the point is bright. When the path difference equals an odd number of half-wavelengths, the peaks meet troughs and the point is dark.

The fringe formula

For a screen placed far away compared with the slit separation, the bright fringes obey a simple formula:

d sin(θ) = m λ

Here d is the distance between the slits, θ is the angle from the centre of the screen to the fringe, λ is the wavelength of the light, and m is an integer: 0 for the central bright spot, 1 for the first bright fringe on each side, 2 for the next, and so on.

Most real setups use angles that are small, so the fringe spacing on the screen can be written even more simply:

y = λ L / d

Here y is the distance between neighbouring bright fringes, L is the distance from the slits to the screen, and d is the slit separation. The result is that fringes are evenly spaced, and the spacing depends on three things: the wavelength, the screen distance and the slit separation.

Worked example with red laser light

Consider a common teaching setup: a helium-neon laser with wavelength 633 nanometres, a screen 1.0 metre away, and different slit separations. The table shows the fringe spacing calculated from y = λL / d.

Slit separation (d)	Fringe spacing (y)
0.05 mm	12.7 mm
0.10 mm	6.3 mm
0.25 mm	2.5 mm
0.50 mm	1.3 mm

Halving the slit separation doubles the spacing. Changing the colour of light to blue, with a wavelength near 450 nanometres, shrinks every fringe spacing by about thirty percent compared with red. This is why interference experiments usually use a narrow band of wavelength, because mixed colours blur the pattern.

Why the central fringe is special

The central bright fringe is the widest and brightest one. Its brightness comes from the fact that the path difference is zero for points directly opposite the midpoint between the slits. Both waves travel the same distance and arrive in phase. As you move away from the centre, the path difference grows, the phase mismatch grows, and the brightness of each fringe falls off. The envelope of the brightness pattern is set by the width of each individual slit, which is a second diffraction effect that sits on top of the interference.

Young's experiment and the case for waves

Thomas Young published his double-slit results in the early 1800s. At the time, many scientists favoured Isaac Newton's view that light is made of particles. An interference pattern cannot be explained by particles simply passing through two holes, because particles would form two bright bands with no fringes between them. Young's pattern showed that light must be a wave, and the wave picture became the standard model for most of the nineteenth century.

James Clerk Maxwell later showed that light is an electromagnetic wave, which gave the interference result a firm theoretical basis.

The quantum twist

The story changed in the twentieth century. Physicists found that the interference pattern persists even when light is made so faint that only one photon passes through the apparatus at a time. Each photon arrives at a single point on the screen, but over time the individual dots build up into the same fringe pattern. The photon seems to interfere with itself.

The same surprise appears with electrons, neutrons and even large molecules. Electrons sent through a double slit one at a time produce an interference pattern made of individual impacts. Experiments of this kind, first carried out with electrons by Claus Jönsson in 1961, show that matter also has wave properties. The wave describes the probability of where each particle lands.

When someone tries to find out which slit a particle passed through, the interference pattern disappears. This link between measurement and pattern is the root of many debates about quantum theory, and it is why the double-slit experiment appears in almost every introduction to the subject.

Practical applications

Interference is not just a classroom demonstration. Thin oil films show coloured bands because light reflects from the top and bottom surfaces and the two reflected waves interfere. Anti-reflection coatings on eyeglasses and camera lenses use thin layers chosen so that reflected waves cancel. Interferometers measure distances to a fraction of a wavelength, and they helped detect gravitational waves by sensing tiny changes in the length of long laser arms.

Diffraction gratings are the many-slit cousin of the double slit. A grating with thousands of lines per millimetre produces sharp, well-separated maxima, and spectroscopists use gratings to identify the chemical elements in stars and lab samples from the colours they emit.

Key takeaways

Two sources of waves overlap, and their amplitudes add. Where peaks line up, the light is bright. Where peaks meet troughs, the light cancels and the spot is dark.

The bright fringes obey d sin(θ) = mλ, and for a distant screen the spacing is y = λL / d. Smaller slit separation and longer wavelength both spread the fringes further apart.

Young's experiment showed that light is a wave. Later experiments with single photons and electrons showed that matter also builds interference patterns, which led to the probability-based picture of quantum physics.

Interference is at work in thin films, anti-reflection coatings, gravitational wave detectors and spectroscopy. The same few lines of algebra explain all of them.