Young's double-slit experiment: why does light behave like a wave?

Imagine sending a laser beam through two thin slits less than half a millimetre apart and letting it fall on a wall a few metres away. You would expect to see two bright lines. Instead, the wall shows a whole row of bright and dark bands side by side. What is more, the spot straight across from the midpoint between the two slits is not dark; it is the brightest place of all. In this post we explain where this surprising pattern comes from, how to calculate it, and what happens when the same experiment is done with one particle at a time.

Is light a wave or a particle? The debate in the early 1800s

In the 1700s the most influential view of light was the one Isaac Newton argued for in Opticks (1704): light is made of tiny particles shot out by the source. Christiaan Huygens, on the other hand, had proposed in 1690 that light spreads like a wave. Both views could explain reflection and refraction; a deciding experiment was needed.

The English physician and physicist Thomas Young put forward the principle of interference for light in a lecture to the Royal Society in 1801. According to Young, two light waves arriving at the same place can strengthen or cancel each other, just like water waves. In an experiment he described in 1803, he split a beam of sunlight with a thin card and saw coloured bands in the card’s shadow. In his textbook published in 1807, he drew an arrangement in which light passes through two small openings. The experiment we now call “Young’s double-slit experiment” comes from this work.

Interference: constructive and destructive

Imagine dipping two fingers in and out of water at the same moment and with the same rhythm. Circular waves spread out from each finger. In some places where these waves meet, two crests land on top of each other and the water rises higher: this is called constructive interference. In other places the crest of one lands on the trough of the other and the two waves cancel: this is called destructive interference. Lines of calm water alternate with lively regions across the surface.

The same happens with two slits. Each slit acts like a source that sends out new waves. The paths that light takes from the two slits to a point on the screen are slightly different. If this path difference is:

• a whole number of wavelengths ($0, \lambda, 2\lambda, \dots$), the two waves meet in step and that point is bright;
• a half-number of wavelengths ($\lambda/2, 3\lambda/2, \dots$), the crest of one wave meets the trough of the other and that point is dark.

The centre of the screen is equally far from both slits, so the path difference there is zero; that is why there is always a bright band in the middle. The wavelength of visible light is between about 380 and 750 nanometres (1 nm is a billionth of a metre). Turning such a tiny length into bands you can measure with a ruler shows the power of the experiment.

How far apart are the fringes?

Let the distance between the slits be $d$, the distance from the slits to the screen $L$, and the wavelength of the light $\lambda$. If the screen is very far from the slits and we look near the centre of the screen (the small-angle approximation), the distance between two neighbouring bright bands is:

Worked example. Let a red helium-neon laser ($\lambda = 632.8$ nm) pass through two slits $d = 0.25$ mm apart, with the screen $L = 1.5$ m away:

The formula tells us three things:

• The longer the wavelength, the more the fringes spread out: red light makes wider fringes than blue light.
• The farther the screen, the more the fringes spread out: the same angles are spread over a wider stretch of a more distant surface.
• The closer the slits, the more the fringes spread out: if $d$ is halved, $\Delta y$ doubles.

The relation also works the other way round: by measuring $d$, $L$ and $\Delta y$ you can work out the wavelength of the light. In 1802 Young himself calculated the wavelengths of colours from measurements of the coloured rings Newton had seen in thin layers.

In the figure below you can change the wavelength, the slit separation, the slit width and the screen distance yourself, and read the fringe spacing off a screen with a millimetre scale.

The single-slit envelope: why don’t the fringes go on for ever?

Real slits have a width. Light passing through one slit of width $a$ also spreads out and leaves a broad hump on the screen, bright in the middle and fading towards the sides. The first dark point of this hump is about $\lambda L / a$ from the centre of the screen. This is called diffraction.

With two slits, the intensity on the screen is the product of the two effects:

The first factor gives the closely spaced fringes from the two slits interfering. The second factor is the single slit’s broad hump, which limits the brightness of the fringes like an envelope. If the slit separation is 5 times the slit width ($d/a = 5$), 9 bright fringes fit inside the central hump; the fifth fringe falls exactly on the hump’s dark point and disappears. The formula rests on the “far-field” and small-angle approximation, which holds when the screen is very far from the slits.

If you close one of the two slits, the interference goes away: the screen shows only the single slit’s broad hump, with no fringes. Places that were dark become lit. In other words, opening a second slit makes less light reach some points of the screen. If we thought of light only as tiny particles, we could not explain this.

Dimming the light to one photon at a time

In the 20th century it became clear that light carries energy in packets called photons. So what does the double-slit experiment look like when the light is dimmed until one photon passes at a time? In 1909 Geoffrey Ingram Taylor photographed the diffraction fringes in the shadow of a needle using light so faint that the exposure lasted months; the fringes were the same as in bright light. Taylor’s light was very weak on average, but it did not guarantee that photons really arrived one by one. In experiments that also showed photons arriving one at a time (for example Grangier, Roger and Aspect, 1986, with a two-arm interferometer), the interference did not disappear.

What happens in these experiments can be summed up like this:

1. Each photon leaves a mark at a single point on the screen; light arrives dot by dot, not as a wave spread over the screen.
2. Where a single photon will land cannot be predicted in advance.
3. As the dots pile up, the fringes predicted by wave theory appear: dots land densely where the bright fringes are and sparsely where the dark fringes are.

In quantum physics this is explained by saying that the probability of each photon landing at a given place on the screen is given by the $|\psi|^2$ distribution that comes from the wave calculation. A single result is random; the distribution of many results is predicted exactly.

Electrons draw the same pattern

Interference is not special to light. In 1924 Louis de Broglie proposed that particles of matter such as electrons also have a wavelength. In 1961 Claus Jönsson sent electrons through very thin, artificially made slits and obtained interference fringes. In 1974 in Bologna, Pier Giorgio Merli, Gian Franco Missiroli and Giulio Pozzi, and in 1989 at the Hitachi laboratory, Akira Tonomura and colleagues sent electrons one at a time. In images from Tonomura’s team, a few dozen electrons look like random dots; once thousands have built up, clear fringes appear. In 2013 Batelaan and colleagues showed the electron double-slit pattern step by step with a set-up in which they could open and close each slit separately.

What happens when we measure “which slit”?

Suppose a detector records which slit each particle went through. Then the fringes do not form. The screen shows the sum of the two humps each slit makes on its own; if the screen is far away, the two humps almost overlap and look like one broad bright patch.

The reason is not a mysterious “observer effect”. Interference comes from adding the contributions (amplitudes) of the two paths. Once the path taken is recorded somewhere, that is, once the two paths become distinguishable, these contributions no longer add together; only the two separate probabilities add, and the interference term drops out. What does this is not that the “detector is a person” or that someone looks at the result; it is that the path information is recorded in some physical system. For example, putting two polarisers at right angles in front of the slits “writes” the path into the light’s polarisation, and the fringes disappear. In the 2002 “quantum eraser” experiment of Walborn and colleagues, when this information was later erased and the measurements sorted accordingly, the fringes could be seen again.

There is one point to be careful about: these experiments do not offer a film of what the particle is “really” doing as it passes through the slits. Quantum physics predicts, with very high accuracy, which results will come out with which probabilities in which set-up; that is what the experiments tell us. How this prediction should be interpreted is still debated among physicists, but the debate does not change the experimental results.

Try it at home: diffraction with a hair

Laser light can damage the eyes. Do this experiment only together with an adult, using a low-power laser pointer (at most 1 mW, labelled “Class 2”); never point the beam at anyone’s eyes, at a mirror or at a shiny surface.

1. Tape a single hair tightly across a hole cut in the middle of a piece of card.
2. Put the card in front of the laser and let the light fall on a light-coloured wall a few metres away.
3. On the wall you will see a bright centre with bands lined up on both sides. The hair behaves like the opposite of a thin slit and makes a similar diffraction pattern.
4. Move the card closer to the wall and farther away: the farther the wall, the more the bands spread out, just like $L$ in the formula $\Delta y = \lambda L / d$.

If you are curious where the colours of light come from, see our lesson on light and mixing colours, and to see how air scatters light depending on its wavelength, read our post on why the sky is blue.

Summary

• In 1801 Thomas Young put forward the principle of interference for light; the bright and dark bands that light from two slits leaves on a screen show that light behaves like a wave.
• If the path difference is a whole number of wavelengths, a bright (constructive) fringe forms; if it is a half-number, a dark (destructive) one.
• The fringe spacing is $\Delta y = \lambda L / d$: it grows with the wavelength and the screen distance and shrinks with the slit separation.
• The width of each slit makes an envelope; the fringes appear inside this single-slit hump.
• When light or electrons are sent one at a time, each lands at a single point; as the dots build up, the same fringes appear.
• Once the slit taken is recorded, the interference term disappears and no fringes form.