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
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
For calculations, show all steps clearly and use the correct units. For comparisons, list both similarities and differences. For explanations, provide clear reasoning and relevant examples.
What the command words demand
- Calculate
- Perform a numerical calculation using given values and formulas.
- Compare
- Identify similarities and differences between two or more items.
- Explain
- Provide a detailed account of how something works or why something happens.
- State
- Give a specific piece of information without elaboration.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate about 5 minutes for each question in this section to ensure you have enough time to complete all parts accurately.
- Identify the given values: D = 2 m , λ = 500 nm = 500 × 10 -9 m .1 mark
- Use the Rayleigh criterion formula: θ = 1.22 × (λ / D) .1 mark
- Substitute the values into the formula: θ = 1.22 × (500 × 10 -9 m / 2 m) .1 mark
- Calculate the result: θ = 1.22 × 250 × 10 -9 .0 marks
- θ = 305 × 10 -9 rad .1 mark
Final answer: 305 × 10 -9 rad
Work through every step correctly and you earn all 4 marks.
Another worked example
A telescope has a collecting power P c that is proportional to the square of its diameter. If the diameter of the telescope is increased from 2 meters to 4 meters, by what factor does the collecting power increase?
- Identify the relationship: P c ∝ D 2 .1 mark
- Calculate the initial and final diameters: D initial = 2 m , D final = 4 m .0 marks
- Determine the ratio of the final diameter to the initial diameter: (D final / D initial ) = (4 m / 2 m) = 2 .1 mark
- Square this ratio to find the factor by which the collecting power increases: (2) 2 = 4 .1 mark
Final answer: 4
Work through every step correctly and you earn all 3 marks.
Common mistakes
Confusing the Rayleigh criterion with other resolution criteria.
Why it happens: Students may mix up different criteria for resolution, such as the Dawes limit or Sparrow's criterion.
Fix: 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.
Why it happens: Students may be more familiar with degrees and forget to convert to radians when using the Rayleigh criterion formula.
Fix: 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.
Why it happens: Students may overlook the relationship P c ∝ D 2 and simply use the diameter without squaring it.
Fix: Double-check that you are using the correct formula: P c ∝ D 2 .
Confusing quantum efficiency with other detector properties.
Why it happens: Students may mix up quantum efficiency with resolution or sensitivity, leading to incorrect comparisons between the human eye and CCDs.
Fix: 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.
Why it happens: Students may use inconsistent units for wavelength and diameter, leading to incorrect results.
Fix: 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.
Why it happens: Students may focus solely on the technical aspects and forget to discuss the practical advantages of CCDs in astronomical observations.
Fix: 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
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Calculate Angular Resolution | Apply the Rayleigh criterion to find the minimum resolvable angle from wavelength and aperture. | 4 |
| Proportionality Ratio | Use the square relationship to find the factor by which collecting power increases. | 3 |
| Quantum Efficiency Comparison | Compare how many photons each detector registers and find the ratio between them. | 4 |
| Calculate Angular Resolution | Find a telescope's minimum angular resolution and convert the result from radians to arcseconds. | 5 |
| Total across these question types | 16 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.