Light interference (Young’s slits)

Superimposing two waves

When two coherent light waves (same frequency, constant phase difference over time) are superimposed, they may add together (constructive interference, bright fringe) or cancel each other out (destructive interference, dark fringe). This is the principle behind Young’s double-slit experiment: a laser source illuminates two narrow, closely spaced slits, which then behave as two secondary coherent sources.

What we observe

On a screen placed at a distance D from the slits (where D is much greater than the slit separation a), we observe a regular alternation of bright and dark fringes: this is the interference pattern.

The fringe spacing

The distance between two consecutive bright fringes, known as the fringe spacing i, is given by:

i = λ × D / a

where λ is the wavelength, D is the distance from the slits to the screen, and a is the distance between the two slits.

Example

Laser wavelength λ = 633 nm, D = 2.00 m, a = 0.50 mm = 5.0 × 10⁻⁴ m: i = (633 × 10⁻⁹ × 2.00) / (5.0 × 10⁻⁴) ≈ 2.5 × 10⁻³ m = 2.5 mm

Common pitfall

Interference patterns are only observed if both sources are coherent (originating from the same initial source). Two independent desk lamps, even if identical, will never produce a stable interference pattern, as their waves are not coherent with one another.