AS 91523 · 2025 paper · interference patterns

Question 3(c) Merit to Excellence

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 double slit is replaced with a diffraction grating whose slits are more closely spaced.

Describe and explain the changes to the interference pattern on the screen.

The 2025 paper, page 9 ↗ Marking schedule, page 7 ↗

Work it out

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

1 What two things change when the double slit becomes a grating?
There are many more slits, and they are closer together: d is smaller.
2 Start with the spacing. What does d sin θ = nλ say about each maximum’s angle when d is smaller?
sin θ = nλ / d, so a smaller d gives a bigger angle for every order. The maxima are further apart and the pattern spreads wider across the screen.
3 Now the brightness. How much light gets through, and how does it add at a maximum?
Many slits let much more of the laser’s light through, and at a maximum the waves from all of them arrive in phase and add. So each maximum is much brighter.
4 Why are the maxima sharper, with wide dark regions between them?
A little to one side of a maximum, neighbouring slits’ waves are only slightly out of step. With two slits that leaves the point fairly bright, so the fringes are broad. Across hundreds of slits those small steps add up, and for each slit there is another whose wave arrives half a cycle behind; they cancel in pairs. So the light falls to nothing very close to each maximum: narrow, well-defined maxima with wide dark regions between.

Answer The maxima are brighter, sharper and further apart. Brighter: many slits let more light through, and at each maximum all their waves arrive in phase. Sharper, with wide dark regions between: just off each maximum the small phase steps between neighbouring slits add up across the grating until the waves cancel. Further apart: the slits are closer together, so by d sin θ = nλ each order sits at a larger angle.

What the marker wanted

Achieved Names one change: brighter, more sharply defined, or maxima further apart.
Merit Gives the reason for one of those three changes.
Excellence All three changes, each with its reason.

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

How did it go?

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