AQA AS Level Physics Paper 2, June 2023: Question 5

1 mark · Medium difficulty · Multiple Choice

Calculate the smallest angle between the third-order and fourth-order maximum diffracted beams for light of wavelength lambda incident normally on a diffraction grating with slit separation 5 lambda.

Practise this question

Question

Multiple choice question 05 states: Light of wavelength lambda is incident normally on a diffraction grating. The separation between adjacent slits is equal to 5 lambda. What is the smallest angle between the third-order maximum and fourth-order maximum diffracted beams? Four options are given: A 13.3 degrees, B 16.2 degrees, C 36.9 degrees, and D 53.1 degrees.
Question text

05 Light of wavelength λ is incident normally on a diffraction grating.

The separation between adjacent slits is equal to 5λ.

What is the smallest angle between the third-order maximum and fourth-order maximum

diffracted beams?

[1 mark]

A 13.3°

B 16.2°

C 36.9°

D 53.1°

Mark scheme

Show the mark scheme Mark scheme table showing question number 05 with key B and answer 16.2 degrees.

Question Key Answer

05 B 16.2°

How to answer it

Diffraction Grating Order Separation

📌 What this question tests

This question assesses your understanding of the diffraction grating equation ( d sin θ = nλ ), rearranging formulas to solve for angles, and finding the difference between consecutive diffraction orders rather than an absolute angle from the central maximum.

Question 05

Determining the angle between the third-order and fourth-order maxima

✅ Correct Answer

B: 16.2°

Awarded 1 mark for selecting option B.

💡 Key Knowledge

  • The grating equation is d sin θ = nλ , where d is slit separation, θ is the angle of diffraction, n is the order, and λ is wavelength.
  • Slit separation is given as d = 5λ .
  • The "smallest angle between" two maxima requires calculating individual angles θ₄ and θ₃ , then finding their difference ( θ₄ - θ₃ ).

🧠 Exam Technique

Read multiple-choice questions carefully. Do not rush to calculate just θ₃ or θ₄ relative to the zero-order beam. The question asks for the angle between the two beams, meaning a subtraction step is mandatory.

❌ Common Errors

  • Direct subtraction of orders: Trying to calculate sin θ = (4 - 3)λ / d directly works as an approximation for very small angles, but fails here because angles are significant and inverse sines are non-linear.
  • Inverting fractions: Accidentally writing sin θ = n / 5 instead of substituting d = 5λ properly.

📐 Step-by-Step Calculation

  1. State the diffraction grating formula:
    d sin θ = nλ
  2. Substitute the given slit separation ( d = 5λ ):
    5λ sin θ = nλ
    Cancel λ from both sides:
    5 sin θ = n  &implies;  sin θ = n / 5
  3. Calculate the angle for the fourth-order maximum ( n = 4 ):
    sin θ₄ = 4 / 5 = 0.8
    θ₄ = sin⁻¹(0.8) = 53.13°
  4. Calculate the angle for the third-order maximum ( n = 3 ):
    sin θ₃ = 3 / 5 = 0.6
    θ₃ = sin⁻¹(0.6) = 36.87°
  5. Find the difference between the angles:
    Δθ = θ₄ - θ₃ = 53.13° - 36.87° = 16.26°
  6. Round to appropriate significant figures:
    16.2° (matches option B).

Topics

Physics · 3.3 Waves

Question and mark scheme from the AQA AS Level Physics examination, Paper 2, June 2023. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.