Analyse the double-slit interference pattern and use the fringe-spacing relationship to determine wavelength.

What this dot point is asking

You need to explain why the double-slit experiment produces an interference pattern and use the fringe-spacing equation to find a wavelength (or another quantity).

Why a pattern forms

Monochromatic light is shone on two narrow slits a small distance $d$ apart. Each slit diffracts the light, so the two slits act as coherent sources (they come from the same wavefront, so they keep a constant phase relationship). The light from the two slits overlaps on a screen a distance $L$ away.

Where the path difference is a whole number of wavelengths, the waves arrive in phase and interfere constructively - a bright fringe. Where it is an odd number of half-wavelengths, they cancel - a dark fringe. The result is a series of evenly spaced bright and dark bands.

The fringe-spacing relationship

For small angles (slits close together, screen far away), the bright fringes are evenly spaced, and the spacing between adjacent fringes is:

This tells you the pattern spreads out (larger $\Delta y$) for:

• longer wavelength (red spreads more than blue),
• a larger screen distance $L$,
• a smaller slit separation $d$.

Why it confirms the wave model

Only waves interfere. The double-slit pattern - alternating bright and dark fringes that depend on wavelength exactly as the wave model predicts - cannot be explained by treating light purely as particles travelling in straight lines. Young's experiment (1801) was decisive evidence for the wave nature of light. (Remarkably, the same pattern appears even when single photons or electrons pass through one at a time - a key clue to wave-particle duality.)