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AS 91523 · 2024 paper · interference

Question 2(c) Merit to Excellence

Practises Diffraction & refraction

Jane's physics teacher shines a red laser through a diffraction grating placed at the centre of a semicircular screen. The pattern on the screen is a number of narrow, bright fringes.

200 lines per mm
λ638 nm

The same red laser is shone through two slits that are the same width as the grating's slits, but further apart.

Describe the differences between the two-slit pattern and the grating's pattern, and explain the reason for each difference.

The 2024 paper, page 4 ↗ Marking schedule, page 3 ↗

Work it out

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

  1. 1 What is different about the two-slit arrangement?

    Two slits instead of hundreds. They are the same width as the grating’s, but further apart: d is larger.

  2. 2 Spacing first. What does d sin θ = nλ do when d is larger?

    sin θ = nλ / d is smaller for every order, so the maxima sit at smaller angles: closer together, over a narrower spread.

  3. 3 Brightness. How much light gets through?

    With just two slits, each no wider than the grating’s, far less light gets through than through hundreds, so the maxima are dimmer.

  4. 4 Sharpness. What happens a little to one side of a maximum?

    With two slits, a point just off a maximum receives two waves only slightly out of phase, which still mostly add, so the brightness fades gradually: broad maxima with fuzzy edges. With a grating, those small phase steps build up across many slits until the waves cancel, so its maxima are narrow and sharp.
Answer The two-slit pattern’s maxima are closer together, dimmer and less sharply defined. Closer: the slits are further apart, so by d sin θ = nλ each order is at a smaller angle. Dimmer: two slits let through much less light than a grating. Less sharp: with only two waves the brightness changes gradually either side of each maximum, while a grating’s many waves cancel just off each maximum.

What the marker wanted

  • Achieved Names one difference: maxima closer together, less bright, or less well defined.
  • Merit Gives the reason for one of those three.
  • Excellence Gives the reasons for all three.

In our words, from NZQA’s 2024 marking schedule.

✕

Common mistake

Calling the whole pattern “diffraction”. NZQA’s 2024 report says diffraction was often used to mean interference: light spreads out of each slit by diffraction, but the bright and dark fringes come from interference between the slits.

How did it go?

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