← Wave Systems: past papers

AS 91523 · 2024 paper · interference

Question 2(d) Merit

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

White light is shone onto the grating. The pattern has a white central region, and the other orders form complete spectra on either side of it.

Explain why white light forms spectra, with violet on the inside and red on the outside, when it passes through a diffraction grating.

The 2024 paper, page 5 ↗ Marking schedule, page 4 ↗

Work it out

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

  1. 1 What is white light made of?

    Every colour, each with its own wavelength: violet the shortest (about 400 nm), red the longest (about 700 nm).

  2. 2 Why is the centre white?

    Straight through, at θ = 0, every colour has zero path difference, so every colour is bright there at once and they mix back into white.

  3. 3 For the first order, what path difference does each colour need?

    One whole wavelength of its own: d sin θ = λ. Violet needs the smallest path difference and red the largest.

  4. 4 So where does each colour’s maximum land?

    sin θ = λ / d, so a smaller wavelength is bright at a smaller angle. Violet’s maximum is nearest the centre and red’s furthest out, and each order spreads into a spectrum from violet on the inside to red on the outside.
Answer White light contains every wavelength, and each colour is bright where d sin θ = nλ for its own λ. At the centre every colour has zero path difference, so it is white. In each order violet has the shortest wavelength, so it needs the smallest path difference and reaches it at the smallest angle: it is on the inside. Red has the longest wavelength, needs the largest path difference, and is on the outside.

What the marker wanted

  • Achieved Says blue (or violet) has the shorter wavelength or path difference, or that red has the longer one.
  • Merit Shows why red sits further out from the central maximum, using the path difference or d sin θ = nλ.

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

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Common mistake

Saying red “diffracts more”. The schedule does not accept it, and NZQA’s 2024 report lists saying that red diffracts more, or blue less, among answers that did not reach Achieved. The colours separate because each needs a different path difference.

How did it go?

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