A student is investigating monochromatic light passing through a double slit. Bright and dark fringes are produced on a screen as shown in [Figure 2.1]. The distance w between 10 bright fringes is measured. The fringe spacing P between neighbouring bright fringes is then determined. The experiment is repeated for light of different wavelengths λ. It is suggested that the fringe spacing P and the wavelength λ are related by the equation P / D = λ / S where D is the distance from the double slit to the screen and s is the slit separation.

Mark scheme

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

1. [1] Gradient = D/S
2. [1] P/mm values: 3.95, 4.35, 4.80, 5.20, 5.55, 5.90
3. [1] Absolute uncertainties in P ± 0.05
4. [1] Six points plotted correctly. Must be within half a small square. Diameter of points must be less than half a small square.
5. [1] Error bars in P plotted correctly. All error bars to be plotted. Total length of bar must be accurate to less than half a small square and symmetrical.
6. [1] Line of best fit drawn. Points must be balanced. Line must pass between (6.45, 5.8) and (6.55, 5.8) and between (4.55, 4.2) and (4.65, 4.2)
7. [1] Worst acceptable line drawn. Steepest or shallowest possible line that passes through all the error bars. Mark scored only if all error bars are plotted.
8. [1] Gradient determined with clear substitution of data points into ∆y/∆x; distance between data points must be at least half the length of the drawn line.
9. [1] Gradient determined of WAL uncertainty = (gradient of line of best fit – gradient of worst acceptable line) or uncertainty = ½ (steepest worst line gradient – shallowest worst line gradient)
10. [1] Substitution of gradient to determine s
11. [1] s = D / gradient (c)(iii)
12. [1] s determined using gradient, given to 2 or 3 significant figures
13. [1] s determined using gradient and correct unit and correct power of ten
14. [1] Percentage uncertainty in s = %uncertainty in D + %uncertainty in gradient or %s = (0.02 / 2.20) * 100 + (∆gradient / gradient) * 100 or correct maximum/minimum method
15. [1] Correct substitution of numbers must be seen, λ in the range 4.05×10⁻⁷ m to 4.24×10⁻⁷ m OR λ = 3.5×10⁻³ / gradient (c)(iii) OR λ = 3.5×10⁻³ x (s / D) = 3.5×10⁻³ x (d)(i) / 2.2
16. [1] Correct substitution of numbers must be seen, Determines absolute uncertainty in λ. Using (c)(iii) uncertainty = ((0.05 / 3.50) + (∆gradient / gradient)) × λ or max λ = (3.55 x 10⁻³ / min gradient), or min λ = (3.45 x 10⁻³ / max gradient) OR Using (d) uncertainty = ((0.05 / 3.50) + (0.02 / 2.20) + (% (d)(i) / 100)) × λ or uncertainty = (0.0234 + (% (d)(i) / 100)) × λ or max λ = (3.55 x 10⁻³ x max s / 2.18), or min λ = (3.45 x 10⁻³ x min s / 2.22)