A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Diffraction Patterns and Gratings — mark scheme explained
The short answer
Diffraction patterns are a fascinating aspect of wave behavior, particularly when light passes through narrow slits or gratings.
The question
A plane transmission grating has a grating spacing of d = 1.5 × 10 -6 m . Monochromatic light with a wavelength of λ = 600 nm is incident on the grating at normal incidence. Calculate the angle of diffraction for the first-order maximum ( n = 1 ). [Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Write down the equation: dsinθ = nλ
- S2
Substitute the given values into the equation: (1.5 × 10 -6 )sinθ = (1)(600 × 10 -9 )
- S3
Simplify the equation: sinθ = (600 × 10 -9 ) / (1.5 × 10 -6 )
- S4
Calculate the value of sinθ: sinθ = 0.4
- S5
Find the angle θ using the inverse sine function: θ = sin -1 (0.4)
- S6
θ ≈ 23.6°
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Write down the equation: dsinθ = nλ
- S2
Substitute the given values into the equation: (1.5 × 10 -6 )sinθ = (1)(600 × 10 -9 )
- S3
Simplify the equation: sinθ = (600 × 10 -9 ) / (1.5 × 10 -6 )
- S4
Calculate the value of sinθ: sinθ = 0.4
- S5
Find the angle θ using the inverse sine function: θ = sin -1 (0.4)
- S6
θ ≈ 23.6°
Final answer: 23.6°
Common mistakes
- Confusing the width of the central maximum with the distance between slits in a diffraction grating. — Clearly distinguish between the slit width (a) in single-slit diffraction and the grating spacing (d) in diffraction gratings. Use the correct equations for each scenario.
- Forgetting to convert units when using the diffraction grating equation. — Always check and convert units before substituting values into equations. Ensure that wavelengths (λ) are in meters and distances (d) are in meters.
- Using the wrong order of maximum (n) in calculations. — Always specify the correct order of the maximum when using the diffraction grating equation. For the first-order maximum, use n = 1.
- Misinterpreting the appearance of the diffraction pattern for white light. — Clearly state that the central maximum is white (all wavelengths overlap there); the side maxima are fringed with colour, with violet/blue nearest the centre and red furthest out (red diffracts most), and the spectra increasingly overlap outward.
- Using the wrong formula for the angular width of the central maximum in single-slit diffraction. — Use the correct formula: θ ≈ (2λ) / a . Ensure that you are calculating the angular width, not the position of the first minimum.
- Forgetting to use the inverse sine function when solving for the angle of diffraction. — Always use the inverse sine function ( sin -1 ) to find the angle of diffraction after solving for sinθ.
Where the marks go
- Full worked solution (all marking points)5 marks