A student is investigating monochromatic light passing through a diffraction grating. A series of maxima are produced on a screen, as shown in Fig. 2.1. [Figure 2.1] The student measures the distance s between the central maximum and the second order maximum on the screen. The experiment is repeated for different wavelengths of light. It is suggested that s and the wavelength λ are related by the equation s² / (s² + D²) = 4N²λ² where D is the distance between the diffraction grating and the screen and N is the number of lines per unit length of the diffraction grating.

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

1. [1] gradient = 1 / (4N²D²)
2. [1] y-intercept = -1 / D²
3. [1] Calculated values for 1/λ² / 10¹²m⁻²: 5.4 or 5.41, 4.3 or 4.34, 3.6 or 3.56, 3.0 or 2.97, 2.6 or 2.60, 2.3 or 2.30
4. [1] Calculated values for 1/s² / m⁻²: 2.6 or 2.60, 1.9 or 1.93, 1.5 or 1.49, 1.2 or 1.18, 0.961 or 0.9612, 0.826 or 0.8264
5. [1] Uncertainties in 1/s² from ± 0.16 or ± 0.17 or ± 0.18 or ± 0.2 to ± 0.02 or ± 0.03.
6. [1] Six points plotted correctly. Must be within half a small square. Diameter of points must be less than half a small square.
7. [1] Error bars in 1/s² plotted correctly. All error bars to be plotted. Length of bar must be accurate to less than half a small square and symmetrical.
8. [1] Line of best fit drawn. Line does not pass through bottom point and line must pass between (4.70, 2.2) and (4.85, 2.2).
9. [1] Worst acceptable line drawn (steepest or shallowest possible line). All error bars must be plotted.
10. [1] Gradient determined with clear substitution of points from the line of best fit into Δy/Δx. Distance between points must be at least half the length of the drawn line.
11. [1] Gradient of worst acceptable line determined. uncertainty = gradient of line of best fit – gradient of worst acceptable line or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient)
12. [1] y-intercept determined by substitution into y = mx + c.
13. [1] y-intercept determined using gradient from worst acceptable line. uncertainty = y-intercept of line of best fit – y-intercept of worst acceptable line or uncertainty = ½ (steepest worst line y-intercept – shallowest worst line y-intercept)
14. [1] D determined using y-intercept and N determined using gradient. D and N given to 2 or 3 significant figures.
15. [1] D determined using y-intercept. D = 1 / √(-y-intercept)
16. [1] N determined using gradient with correct power of ten and units. Correct substitution of numbers must be seen. N = 1 / (√(4 × gradient × D²)) or N = √(-y-intercept) / (2 × √gradient)
17. [1] Percentage uncertainty in N determined. Correct substitution of numbers must be seen. % uncertainty in N = ½ (% uncertainty in gradient + 2 × % uncertainty in D) or % uncertainty in N = ½ (% uncertainty in gradient + % uncertainty in y-intercept)