Explain diffraction, two-slit interference and the electromagnetic spectrum as evidence for the wave model of light

What this dot point is asking

WACE wants you to use diffraction and two-slit interference as the historical and quantitative evidence that light is a wave, work with the path-difference conditions and the fringe-spacing formula, and place visible light within the broader electromagnetic spectrum. The skill being tested is connecting the geometry of the slits to the observed pattern.

Diffraction

Diffraction is the spreading of a wave as it passes an edge or through a gap. The effect is significant when the gap width is similar to or smaller than the wavelength: a wide gap gives little spreading, a narrow gap gives a lot. Because visible light has a tiny wavelength (hundreds of nanometres), noticeable diffraction needs very narrow slits, which is why everyday light appears to travel in straight lines.

Two-slit interference

In Young's experiment, monochromatic light illuminates two narrow, closely spaced slits that act as coherent sources. The diffracted light from each slit overlaps and superposes, producing alternating bright and dark fringes on a distant screen. Bright fringes (constructive interference) occur where the path difference is a whole number of wavelengths,

Dark fringes (destructive interference) occur at half-integer multiples, $d\sin\theta=(m+\tfrac{1}{2})\lambda$. Here $d$ is the slit separation and $\theta$ the angle to the fringe.

Fringe spacing

For small angles and a screen a distance $L$ away, the spacing between adjacent bright fringes is

So fringes spread out for longer wavelengths (red), a more distant screen, or closer slits. Measuring $\Delta y$, $L$ and $d$ lets you calculate the wavelength of light, which is how the experiment first pinned down $\lambda$ for visible light.

Coherence and monochromatic light

A clear pattern needs coherent sources: a constant phase relationship and a single wavelength. This is why a single source illuminating two slits (or a laser) works, while two independent lamps do not. White light produces overlapping coloured fringes because each wavelength has its own spacing.

The electromagnetic spectrum

Light is one part of a continuous spectrum of electromagnetic waves, all travelling in vacuum at $c=3.0\times10^{8}\ \text{m s}^{-1}$ and all obeying $c=f\lambda$. In order of increasing frequency (decreasing wavelength) the spectrum runs radio, microwave, infrared, visible, ultraviolet, X-ray and gamma. Visible light occupies only a narrow band from about $400\ \text{nm}$ (violet) to $700\ \text{nm}$ (red). All these waves are transverse oscillations of electric and magnetic fields.

Keeping the units straight

Slit separations are millimetres, fringe spacings millimetres, wavelengths nanometres, and the screen distance metres. Convert everything to metres before substituting, and decide whether a question is asking for a fringe position (use $d\sin\theta=m\lambda$) or a spacing (use $\Delta y=\frac{\lambda L}{d}$).