Last updated: 2026-06-16

Young's double-slit experiment

Thomas Young's 1801 experiment provided decisive evidence that light behaves as a wave. By passing a beam of light through two closely spaced slits, Young observed alternating bright and dark bands — an interference pattern — on a screen beyond the slits. The existence of dark bands, where light from two sources cancels, is impossible to explain if light consists of particles alone.

The same wave-optics framework describes interference in thin films, diffraction gratings, and the design of anti-reflection coatings, making the double-slit result a foundation of classical optics.

How the pattern forms

Each slit diffracts the incoming light, acting as a secondary source of circular waves. Light from the two slits travels different distances to reach any point on the screen. This difference in path length — called the path difference — determines whether the waves reinforce or cancel.

At a point on the screen making angle $\theta$ with the forward direction, the path difference is $d\sin\theta$, where $d$ is the centre-to-centre slit separation. Two conditions follow:

• Bright fringe (constructive interference): the path difference is a whole number of wavelengths,

$d\sin\theta = m\lambda, \quad m = 0,\,1,\,2,\dots$

• Dark fringe (destructive interference): the path difference is a half-integer number of wavelengths,

$d\sin\theta = \left(m - \tfrac{1}{2}\right)\lambda.$

The integer $m$ is the fringe order. The central bright fringe at $\theta = 0$ has order zero; the first bright fringes on either side have order one, and so on.

Formulas

Here $L$ is the distance from the slits to the screen. The fringe spacing $\Delta y$ is the same between any two adjacent bright fringes and does not depend on which order is examined.

Small-angle approximation

When $d \gg \lambda$ the fringe angle $\theta_m$ is small, so $\sin\theta \approx \tan\theta \approx \theta$ (in radians). The position of the m-th bright fringe then simplifies to

$y_m \approx \frac{m\lambda L}{d},$

and the fringe spacing becomes

$\Delta y = \frac{\lambda L}{d}.$

This calculator uses the exact formula (arcsin and tan), but the small-angle result is accurate to better than one part in a thousand whenever $\theta < 5°$.

Worked example

A green laser ($\lambda = 550\ \text{nm}$) illuminates a double slit with separation $d = 0.25\ \text{mm}$. A screen is placed $L = 2\ \text{m}$ away.

Fringe spacing:

$\Delta y = \frac{\lambda L}{d} = \frac{(550 \times 10^{-9})(2)}{0.25 \times 10^{-3}} = 4.4\ \text{mm}.$

Position of the first bright fringe (order $m\!=\!1$):

$\sin\theta_1 = \frac{\lambda}{d} = \frac{550 \times 10^{-9}}{0.25 \times 10^{-3}} = 2.2 \times 10^{-3},$

$y_1 = L\tan(\arcsin(2.2 \times 10^{-3})) \approx 4.4\ \text{mm},$

consistent with the fringe spacing for this small angle.

Requirement for coherent light

The interference pattern is stable only when the two slit sources maintain a constant phase relationship — that is, when the light is coherent. A laser is inherently coherent. Young achieved coherence with a single narrow slit upstream of the double slit so both secondary sources drew from the same wavefront. Ordinary white light produces a superposition of patterns from every wavelength in the spectrum; only a few coloured fringes near the centre are visible before they wash out.

Applications

Double-slit interference underpins several areas of technology and science:

• Interferometry — measuring tiny displacements or refractive-index differences with sub-wavelength precision.
• Holography — recording three-dimensional wavefronts as interference patterns.
• Anti-reflection coatings — engineering thin-film path differences to cancel unwanted reflections.
• Quantum mechanics — the same experiment performed with single electrons or atoms demonstrates the wave nature of matter (wave–particle duality).

Limits of the model

This calculator assumes monochromatic, coherent plane-wave illumination and infinitely thin slits of equal width. Real experiments show additional modulation by the single-slit diffraction envelope, which suppresses certain orders. The formula also breaks down when $m\lambda > d$ because no angle exists with $\sin\theta > 1$; the calculator flags this condition.