Apply path difference and the double-slit equation to analyse two-source interference of light

What this dot point is asking

WACE wants you to apply the interference conditions, use the fringe-spacing equation, and explain why two-slit interference cannot be accounted for by treating light as particles. Coherence is the key requirement: the two sources must keep a fixed phase relationship.

Coherent sources and path difference

When light passes through two slits a distance $d$ apart, each slit acts as a source. Because they come from the same original beam, they are coherent. At a point on the screen the two waves have travelled slightly different distances; this path difference determines whether they arrive in step or out of step.

Bright and dark fringes

Constructive interference (a bright fringe) occurs when the path difference is a whole number of wavelengths,

Destructive interference (a dark fringe) occurs when the path difference is a half-integer number of wavelengths,

The central bright fringe ($m=0$) sits directly opposite the midpoint of the slits, where the path difference is zero.

Fringe spacing on the screen

For small angles and a screen a distance $L$ from the slits, the bright fringes are evenly spaced by

This shows that closer slits or a longer screen distance spread the fringes further apart, and that longer-wavelength light gives wider fringes. Measuring $\Delta y$ is a standard way to determine the wavelength of light.

Why this proves light is a wave

Particles cannot cancel each other, but waves can: the dark fringes are places where light plus light gives darkness through destructive interference. Only a wave model explains alternating bright and dark bands, so Young's experiment was the historic confirmation of the wave nature of light.

Keeping the conditions straight

Use $d\sin\theta=m\lambda$ for bright fringes and the half-integer version for dark, and use $\Delta y=\lambda L/d$ for spacing on the screen. Convert slit separations from millimetres to metres and keep the screen distance in metres. The order number $m$ counts fringes out from the centre.