A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Minimum Angular Resolution and Detector Comparison in Telescopes — mark scheme explained
The short answer
In this section, we will explore the minimum angular resolution of telescopes, the Rayleigh criterion, and how the collecting power relates to the diameter of the telescope. We will also compare the eye and CCD (Charge-Coupled Device) as detectors in terms of quantum efficiency, resolution, and convenience of use.
The question
A telescope with a diameter of 2 meters is used to observe two stars. If the wavelength of light is 500 nm, calculate the minimum angular resolution θ in radians. [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
Identify the given values: D = 2 m , λ = 500 nm = 500 × 10 -9 m .
- S2
Use the Rayleigh criterion formula: θ = 1.22 × (λ / D) .
- S3
Substitute the values into the formula: θ = 1.22 × (500 × 10 -9 m / 2 m) .
- S4
Calculate the result: θ = 1.22 × 250 × 10 -9 .
- S5
θ = 305 × 10 -9 rad .
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Identify the given values: D = 2 m , λ = 500 nm = 500 × 10 -9 m .
- S2
Use the Rayleigh criterion formula: θ = 1.22 × (λ / D) .
- S3
Substitute the values into the formula: θ = 1.22 × (500 × 10 -9 m / 2 m) .
- S4
Calculate the result: θ = 1.22 × 250 × 10 -9 .
- S5
θ = 305 × 10 -9 rad .
Final answer: 305 × 10 -9 rad
Common mistakes
- Confusing the Rayleigh criterion with other resolution criteria. — Review and memorize the specific formula for the Rayleigh criterion: θ = 1.22 × (λ / D) .
- Using degrees instead of radians in calculations involving angular resolution. — Always use radians for angle measurements in this context. Remember that 1 radian ≈ 57.3 degrees.
- Forgetting to square the diameter when calculating collecting power. — Double-check that you are using the correct formula: P c ∝ D 2 .
- Confusing quantum efficiency with other detector properties. — Understand that quantum efficiency (QE) is specifically about the ratio of detected photons to incident photons. Review the definitions and differences between QE, resolution, and sensitivity.
- Failing to convert units correctly when using the Rayleigh criterion formula. — Ensure that all units are consistent. Convert wavelengths from nanometers to meters before using them in the formula: θ = 1.22 × (λ / D) .
- Overlooking the practical implications of using CCDs over the human eye. — Include a discussion of the practical benefits of CCDs, such as higher quantum efficiency, better resolution, and greater convenience for long-term data collection.
Where the marks go
- Full worked solution (all marking points)4 marks