Young’s slits: fringe spacing and interference pattern

Young’s double-slit experiment

Two narrow slits, S1 and S2, separated by a distance a, are illuminated by the same coherent point source. They behave as two secondary sources in phase. On a screen placed at a distance D >> a, an alternating pattern of bright and dark fringes is observed.

Position of the fringes and fringe spacing

For a point M identified by its x-coordinate on the screen (where x is small compared to D), the phase difference is approximately:

delta = a*x/D

The bright fringes (maxima) appear for x_p = plambdaD/a, where p is an integer (order of interference). The fringe spacing, the distance between two consecutive bright fringes, is given by:

i = lambda*D/a

Quantity	Symbol	Effect of an increase
Screen-to-slits distance	D	increases i
Slit separation	a	decreases i
Wavelength	λ	increases i

Observed intensity

I(x) = 4I₀cos²(πax/(λ*D))

Common pitfall

The formula x_p = pλD/a assumes the small-angle approximation (where a and x are very small compared to D): it becomes incorrect if a is no longer much smaller than D, or if the slits are not sufficiently narrow (the diffraction specific to each slit then modulates the intensity of the fringes).