AQA A-Level Physics Paper 1, June 2022: Question 20

✅ Correct Answer: D

Option D ( 2.2 × 10⁻⁴ m ) is the correct slit separation.

💡 Key Knowledge

• The Equation: w = λD / s where w is fringe width, λ is wavelength, D is slit-to-screen distance, and s is slit separation.
• Rearranging for slit separation s gives: s = λD / w .

📐 Step-by-Step Calculation

1. Extract parameters:
   Wavelength ( λ ) = 5.2 × 10⁻⁷ m
   Distance ( D ) = 1.5 m
2. Find single fringe width ( w ):
   The width of ten fringes = 3.5 cm .
   Therefore, w = 3.5 cm / 10 = 0.35 cm .
3. Convert units to metres:
   0.35 cm = 0.35 × 10⁻² m (or 3.5 × 10⁻³ m ).
4. Rearrange and substitute into the formula:
   s = (5.2 × 10⁻⁷ × 1.5) / (3.5 × 10⁻³)
   s = 7.8 × 10⁻⁷ / 3.5 × 10⁻³
   s = 2.2285 × 10⁻⁴ m ≈ 2.2 × 10⁻⁴ m .

❌ Common Errors & Traps

• Fringe Count Trap: Forgetting to divide the 3.5 cm measurement by 10. Using 3.5 cm directly as w leads to option A ( 2.2 × 10⁻⁵ m ).
• Unit Conversion Errors: Forgetting to convert centimetres into metres (missing the ×10⁻² multiplier), which throws off powers of ten significantly.
• Powers of Ten Mistakes: Entering numbers incorrectly into the calculator when handling multiple negative indices. Always double-check standard form entries!