Testing double-slit fringe spacing

Part (a) marking points

Final answer: 6.0 × 10^-7 m. Numerical checks assess the final value only; they do not check working or the number of digits typed.

1. Convert gradient to 0.0020 m m⁻¹ and slit separation to 0.00030 m. (1 method mark)
2. Use λ = gradient × s = 6.0 × 10^-7 m. (1 accuracy mark)

No earlier numerical result is required. Award method credit for valid working and accuracy credit for the stated answer. Accept a defensible equivalent method; wrong physics cannot earn dependent accuracy credit.

Common errors: Use λ = gradient × slit separation, not divide.

Part (b) marking points

Final answer: 3.6 × 10^-3 m. Numerical checks assess the final value only; they do not check working or the number of digits typed.

1. Use w = λD/s with unrounded working. (1 method mark)
2. Obtain 3.6 × 10^-3 m. (1 accuracy mark)

Use the wavelength from part (a) in w = λD/s with D = 1.8 m and s = 0.00030 m.

Common errors: Convert slit separation from millimetres to metres.

Part (c) marking points

1. The same endpoint reading uncertainty applies to a larger measured distance. (1 independent mark)
2. Dividing by ten reduces the absolute uncertainty per interval; count intervals, not bright fringes. (1 independent mark)

Award each distinct physical point once. Equivalent scientifically correct wording is creditable; a contradictory statement cannot earn the same point.

Part (d) marking points

1. At a given angle, path difference is proportional to slit separation. (1 independent mark)
2. The angle needed for one-wavelength path difference is smaller, so adjacent fringes are closer. (1 independent mark)

Award each distinct physical point once. Equivalent scientifically correct wording is creditable; a contradictory statement cannot earn the same point.

Acceptable alternatives: Use w = λD/s at fixed λ and D to show half the spacing; a physical path-difference explanation is needed for the second point.