Question 2(b) Merit to Excellence

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.

The grating has 200 lines per mm, and the laser's wavelength is 638 nm. Calculate the total number of dots seen on the semicircular screen, beginning with the distance between the slits.

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 Start with the slit spacing. 200 lines per millimetre is how many per metre?

   200 × 1000 = 200 000 lines per metre, so d = 1 / 200 000 = 5.00 × 10⁻⁶ m.

2. 2 The screen is a semicircle around the grating. What is the largest angle a maximum could reach?

   90° either side: the screen catches every order the grating makes. At 90°, sin θ = 1.

3. 3 What is the highest order?

   n = d sin 90° / λ = 5.00 × 10⁻⁶ / 638 × 10⁻⁹ = 7.837. An order has to be a whole number, so round down: the highest is n = 7.

4. 4 Count every dot.

   Seven orders on each side of the central dot, plus the central dot itself (n = 0): 7 + 7 + 1 = 15.

What the marker wanted

• Achieved The right slit spacing, 5 × 10⁻⁶ m; or nλ = d sin θ and 2n + 1 used, with the values put in correctly but the wrong d.
• Merit n = 7.83, or the whole calculation with one error.
• Excellence 15 dots, with the central maximum counted.

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

Common mistake

How did it go?

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