AQA A-Level Physics Paper 1, June 2023: Question 16

1 mark · Medium difficulty · Multiple Choice

Determine which combination of slit separation and wavelength produces a fringe spacing of 1.5w when the slit-to-screen distance is halved.

Practise this question

Question

Multiple choice question 16 asking to identify the correct combination of slit separation and wavelength from a table with options A to D, given changes to double slit interference parameters.
Question text

16 A double slit with a separation s is illuminated by light of wavelength λ.

Fringes with spacing w are produced on a screen placed a distance D from the slits.

D

The distance from the slits to the screen is changed to .

Which combination of slit separation and wavelength produces a fringe spacing of 1.5w on

the screen?

[1 mark]

Slit separation Wavelength

A 0.22s 0.66λ

B 0.50s 0.75λ

C 0.60s 1.20λ

D 1.20s 0.40λ

Mark scheme

Show the mark scheme Mark scheme indicating that option A is the correct answer, with slit separation 0.22s and wavelength 0.66 lambda.

16 A 0.22s 0.66λ

How to answer it

Double Slit Interference Proportions

Question 16 • Multiple Choice • 1 Mark

What this question tests

This question assesses your ability to manipulate standard wave equations, specifically understanding proportional relationships between fringe spacing ( w ), wavelength ( λ ), slit separation ( s ), and slit-to-screen distance ( D ). It tests multi-variable proportional reasoning under changed conditions.

Question 16 Solution Guide

Analysing the Double Slit Equation

💡 Key Knowledge

  • The double slit fringe spacing equation is: w = λD / s
  • Direct proportionality: w increases with λ and D .
  • Inverse proportionality: w decreases as s increases.

✅ Correct Answer: A

Option A ( 0.22s slit separation and 0.66λ wavelength) correctly yields the target 1.5w fringe spacing when distance is halved.

🧠 Exam Technique

Set up an initial equation, substitute the altered variables into the formula, and test the options algebraically rather than guessing. Look for the ratio that balances the equation to equal 1.5.

❌ Common Errors

Forgetting to account for the halved distance ( D / 2 ) in the numerator, or inverting the slit separation ( s ) relationship by multiplying instead of dividing.

📐 Step-by-Step Calculation & Proportional Breakdown

  1. Write the initial relationship: w = λD / s
  2. Apply the change to distance: The new distance is D / 2 . Let the new fringe spacing be w_new = 1.5w .
  3. Set up the proportionality expression:
    New equation: 1.5w = (λ_new × (D / 2)) / s_new
  4. Rearrange to find the required ratio of ( λ_new / s_new ):
    Substitute w = λD / s into the left side:
    1.5 × (λD / s) = (λ_new × D) / (2 × s_new)
  5. Cancel D from both sides:
    1.5 × (λ / s) = λ_new / (2 × s_new)
  6. Test Option A ( s_new = 0.22s and λ_new = 0.66λ ):
    Right hand side becomes: 0.66λ / (2 × 0.22s) = 0.66λ / 0.44s = 1.5 × (λ / s) .
    This matches the target exactly!
Mark Scheme Award: 1 mark for selecting option A.

Topics

Physics · 3.3 Waves

Question and mark scheme from the AQA A-Level Physics examination, Paper 1, June 2023. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.