Result

Single-slit diffraction

a sin θ = mλ (dark fringes, m = 1, 2, 3, \dots)

Statement

The angles at which dark fringes appear for a single slit of width a.

Symbols and units

$a$	slit width	m
$θ$	angle from the centre line	degrees
$m$	dark-fringe order	—
$λ$	wavelength	m

When it applies

Coherent, monochromatic light through a single slit; far-field (Fraunhofer) diffraction.

Don't use when

Locates dark fringes, the opposite of the double-slit formula, which locates bright fringes — mixing the two up is a common error.

Derivation

Dividing the slit into pairs of sub-sources that cancel in pairs gives the condition for destructive interference, located at:

a sin θ = mλ

Watch out for

For a single slit, this locates DARK fringes — the opposite of the double-slit condition, where the analogous formula gives bright fringes. Mixing the two up is a common mistake.

Connects to

Double-slit fringe condition