AS 91523 · 2025 paper · interference patterns

Question 3(b) Merit

A laser shines green light onto a double slit of separation 1.25 × 10⁻⁴ m. Each slit acts as a light source in phase with the other, giving an interference pattern of closely spaced fringes on a screen. With the screen 3.40 m from the slits, the distance from the central maximum to the 3rd-order maximum is 4.20 × 10⁻² m.

d	1.25×10⁻⁴ m
L	3.40 m
x (centre to 3rd order)	4.20×10⁻² m

The paper shows a photo of the pattern from the two slits: a row of bright green fringes with dark gaps between them.

Explain why the intensity of the light on the screen varies like this.

The 2025 paper, page 8 ↗ Marking schedule, page 7 ↗

See it move: Two sources, and the path difference between them

Work it out

Try it on paper first. Stuck? Take one hint at a time.

1 Light from both slits reaches every point on the screen. What is different about the two journeys to one point?
Their lengths. Except at the very centre, the light from one slit travels further than the light from the other: there is a path difference.
2 The slits send their light out in phase. Where one path is longer by exactly nλ (n = 0, 1, 2, …), how do the two waves arrive?
Still in phase: a phase difference of 360°, or a whole number of cycles. They superpose constructively into a large amplitude, so the point is bright.
3 And where one path is longer by (n + ½)λ?
Exactly out of phase, 180° apart. They superpose destructively and cancel, so the point is dark.
4 Why does the brightness keep alternating as you move along the screen?
Moving outwards, the path difference grows steadily through 0, ½λ, λ, 1½λ, and so on, so the two waves keep switching between arriving in phase and out of phase. In between those points they partly cancel, so the brightness changes smoothly from bright to dark.

Answer The light from the two slits travels different distances to each point on the screen. Where one path is longer by nλ, a whole number of wavelengths, the waves arrive in phase and superpose constructively: a bright fringe. Where it is (n + ½)λ, they arrive 180° out of phase and cancel: a dark gap. The path difference grows steadily along the screen, so bright and dark fringes alternate.

What the marker wanted

Achieved Explains the changing brightness through the path difference, or the phase difference, or the superposition it leads to.
Merit Links the path difference (or phase difference) to the superposition it causes: in phase and constructive gives bright, out of phase and destructive gives dark.

In our words, from NZQA’s 2025 marking schedule.

Common mistake

Explaining the fringes with diffraction, or only with “peaks and troughs”. NZQA’s 2025 report names both: the fringes come from interference between the two slits’ light, and a Level 3 answer gives the path difference and the phase it leads to.

How did it go?

Got it moves it further out. Review brings it back tomorrow.