Finding a wavelength from diffraction orders

10 marks · A-level · original practice case

Write your working and explanations below or on paper. Your responses stay in this page; PhysicsHelp does not submit or save them. Copy anything you want to keep before closing it. Check calculations separately from method marks. Use unrounded working between parts.

The situation

A laser illuminates a diffraction grating normally. The grating has 300 lines per millimetre. Angles to the central maximum are measured on both sides; the table gives simulated magnitudes. The small difference between left and right readings may arise from an angular zero offset. Wear suitable eye protection and do not view the beam directly.

Diffraction maxima
Order n	Left angle / °	Right angle / °
1	10.9	11.1
2	22.3	22.5
3	34.7	34.9
4	49.3	49.5

Part (a)

Construct a graph from these readings that can be used to determine wavelength. Explain your choice of variables. Draw the graph on paper. [3 marks]

Your explanation

Part (b)

Determine the wavelength using your graph. [3 marks]

Give the numerical answer to 3 significant figures. Graph readings between 6.2 × 10^-7 and 6.5 × 10^-7 m are accepted.

Final value / m

Working

Part (c)

Determine the highest possible diffraction order for this wavelength. [2 marks]

Give the numerical answer to 1 significant figures.

Final value (no unit)

Working

Part (d)

Explain the benefit and limitation of averaging left and right angle magnitudes. [2 marks]

Your explanation

Marking rubric and worked answers

One example fit. Small differences in graph readings are expected; use the accepted range in the rubric.

Indicative practice marks. Method marks assess valid working; accuracy marks require the associated valid method. Independent points stand on their own. Tick only points supported by your response. Do not award the same explanation twice. These ticks record your judgement, not an examiner’s result.

Part (a) marking points

Average each pair of angle magnitudes to obtain 11.0°, 22.4°, 34.8°, 49.4°; calculate their sines. (1 independent mark)
From d sin θ = nλ, plot sin θ vertically against n horizontally; label dimensionless axes and use a suitable linear scale. (1 independent mark)
Plot about 0.191, 0.381, 0.571 and 0.759 and draw a best-fit straight line; determine a gradient from widely separated points. (1 independent mark)

Credit equivalent correct explanations. Award each distinct point once; a contradiction invalidates the affected point.

Acceptable alternatives: Plot n vertically against sin θ and invert the gradient consistently.

Part (b) marking points

Final answer: 6.33 × 10^-7 m. Numerical checks assess the final value only; they do not check working or the number of digits typed.

Convert line density to grating spacing d = 1/(300 × 1000) m. (1 method mark)
Use λ = d × gradient, about (3.33 × 10^-6) × 0.190. (1 method mark)
Obtain a value in the accepted range 6.2 × 10^-7–6.5 × 10^-7 m. (1 accuracy mark)

Credit a defensible fitted gradient in the accepted range. Carry forward an arithmetic error in the student’s gradient for method credit, but retain the stated range for full accuracy credit.

Acceptable alternatives: For reversed axes use λ = d/gradient. Individual order calculations near 633 nm can corroborate, but do not replace the requested graph.

Part (c) marking points

Final answer: 5 (no unit). Numerical checks assess the final value only; they do not check working or the number of digits typed.

A maximum requires nλ/d ≤ 1. (1 method mark)
Use floor(d/λ) = 5; a sixth order would require sin θ > 1. (1 accuracy mark)

Use the student’s physically plausible wavelength from part (b) to determine the greatest permitted integer n. A non-integer highest order cannot earn the accuracy mark.

Part (d) marking points

A small common angular zero offset increases one magnitude and decreases the other, so their mean removes that offset when both are measured from the same reference. (1 independent mark)
It does not remove a shared scale calibration error or guarantee normal incidence; alignment and grating spacing still require checks. (1 independent mark)

Credit equivalent correct explanations. Award each distinct point once; a contradiction invalidates the affected point.

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Related skills

Scope and reference sources

AQA 3.3.2.2; OCR A 4.4.3 with practical/mathematical skills. These are shared original exercises; wording, indicative marks and difficulty have not been endorsed by either board.

AQA specification · OCR A specification

Case reference: diffraction-orders-fit · version 1.1.0 · seed 0. Choose another case