Double-slit experiment

Thomas Young's interference experiments, presented from 1803 (the two-slit form appears in his 1807 Lectures), send light from one source through two narrow slits and observe the pattern on a screen beyond. Instead of two bright lines, the screen shows a series of evenly spaced fringes. Each slit acts as a source of diffracted waves, and where the two waves overlap their path difference to each point on the screen decides whether they add or cancel: the pattern is two-beam interference. The experiment was strong early evidence for the wave nature of light.

Fringe spacing

For slits separated by $d$ and a screen at distance $L \gg d$, bright fringes occur where the path difference $d\sin\theta$ is a whole number of wavelengths, and on the screen they are spaced by

With 632.8 nm light, slits 0.25 mm apart and a screen 1 m away, the spacing is 2.53 mm. The fringes are modulated by the single-slit diffraction envelope of each slit of width $a$, whose first zero lies at $\lambda L/a$ from the centre: for 0.05 mm slits, 12.7 mm, so about nine fringes fit inside the central envelope. The far-field condition is a small Fresnel number for each slit; a lens placed after the slits puts the same pattern in its focal plane at any distance.

Coherence

Fringes appear only if the light at the two slits is mutually coherent. Young used sunlight passed through a pinhole, which made the illumination spatially coherent across the slits; with an extended source, the fringes wash out once the slits are farther apart than the transverse coherence width. With broadband light only a few fringes near the centre survive, because the path difference soon exceeds the coherence length, and each colour forms fringes of a different spacing. A laser shows many sharp fringes.

One photon at a time

When the source is attenuated so that only one photon is in the apparatus at a time, each photon arrives at a single point on the detector, yet the accumulated arrivals form the same fringe pattern. G. I. Taylor reported fringes at very low intensity in 1909, and single-photon and single-electron versions with modern detectors show the build-up point by point. Any measurement that determines which slit each photon passed through destroys the fringes. The experiment is the standard illustration of wave-particle duality and of the photon statistics of detection.

In the lab

The double-slit arrangement is a simple way to measure spatial coherence, by recording fringe visibility as a function of slit separation, or to measure wavelength from the fringe spacing. It is also the basis of stellar interferometry, where the slits become separated telescopes.

The slit diffraction calculator draws the two-slit pattern for chosen slit widths, spacing, wavelength and screen distance, with the single-slit envelope and any missing orders.

References: T. Young, Phil. Trans. R. Soc. Lond. 94, 1 (1804); G. I. Taylor, Proc. Camb. Phil. Soc. 15, 114 (1909); E. Hecht, Optics, 5th ed. (Pearson, 2017), Ch. 9.