Result

Double-slit fringe condition

d sin θ = mλ (bright fringes)

Statement

The angles at which bright fringes appear, for slits separated by distance d.

Symbols and units

$d$	slit separation	m
$θ$	angle from the centre line	degrees
$m$	fringe order	—
$λ$	wavelength	m

When it applies

Coherent, monochromatic light; slit separation and screen distance such that the small-angle (or far-field) approximation holds.

Don't use when

This locates bright fringes only — dark fringes fall at half-integer multiples instead; also requires the small-angle/far-field approximation to hold.

Derivation

The path difference between the two slits, viewed at angle θ, is d sin θ; setting this equal to a whole number of wavelengths gives constructive interference:

d sin θ = mλ

Worked examples

Why closer slits give wider fringes

Fringe spacing on a distant screen follows from the small-angle form of the fringe condition:

Δ y \approx \frac{λ L}{d}

Fringe spacing is inversely proportional to slit separation d — narrowing the slit spacing spreads the pattern out, the opposite of what intuition often suggests.

Watch out for

This locates the BRIGHT fringes; dark fringes fall at half-integer multiples, d sin θ = (m + ½)λ. Fringe spacing is inversely proportional to slit separation — closer slits produce WIDER-spaced fringes, the opposite of what intuition suggests.