AQA A-Level Physics Paper 3 (3BA), June 2025: Question 2

10 marks · Hard difficulty · Extended Answer

Draw a ray diagram for an astronomical telescope, compare a refracting and reflecting telescope observing Mars, and explain advantages of a CCD over the human eye.

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Question

Question 02 has three parts. Part 02.1 asks to draw a ray diagram for an astronomical telescope in normal adjustment, including three non-axial rays and labelled principal foci for the lenses (2 marks). Part 02.2 presents Table 1 with data for two telescopes: Telescope A is a refractor with objective diameter 0.12 m and angular magnification 25; Telescope B is a reflector with objective diameter 0.18 m and angular magnification 40. Additional data provided: diameter of Mars = 6.8 × 10³ km, distance = 0.55 AU, angular resolution of the eye ≈ 3 × 10⁻⁴ rad. It asks to compare the images formed by A and B, referring to relative brightness, ability to show features on Mars, and effects of aberrations (6 marks). Part 02.3 asks to explain two advantages of using a CCD rather than the eye when making an observation (2 marks).
Question text

02.1 Draw a ray diagram for an astronomical telescope in normal adjustment.

Include in your diagram:

• three non-axial rays

• labelled principal foci for the lenses.

[2 marks]

02.2 An astronomer has two telescopes A and B.

The astronomer uses each telescope to make observations of Mars when Mars

is 0.55 AU from the Earth.

Table 1 gives information about A and B.

Table 1

Telescope Type Objective diameter / m Angular magnification

A refractor 0.12 25

B reflector 0.18 40

diameter of Mars = 6.8 × 103 km

angular resolution of the eye ≈ 3 × 10−4 rad

Compare the images formed by A and B.

In your answer, refer to:

• the relative brightness of the images

• the ability of each telescope to show features on Mars

• the effect of any aberrations caused by each type of telescope.

[6 marks]

02.3 One advantage of using a CCD with a telescope is that the data can be stored and

processed on a computer.

*04Explain* two other advantages of using a CCD rather than the eye when making an

observation with a telescope.

[2 marks]

Mark scheme

Show the mark scheme Mark scheme for Question 02: 02.1 awards 2 marks for a correct diagram with three non-axial rays crossing at the common focal plane and emerging parallel from the eyepiece, with principal foci Fo and Fe labelled at a coincident point closer to the eyepiece. 02.2 is a 6-mark level-of-response question covering relative brightness (collecting power proportional to diameter squared, B is 2.25 times brighter), showing features (angular size of Mars, Rayleigh criterion/diffraction limit, and angular magnification vs eye resolution), and aberrations (chromatic aberration in refractor A, parabolic mirror in B avoids spherical aberration). 02.3 awards 2 marks for two explained advantages of CCDs: higher quantum efficiency, smaller pixel size providing higher resolution, detection outside the visible spectrum, or ability to integrate light over longer exposures.

Question Answers Additional comments/Guidance Mark AO

02.1 Diagram correct with a set of three non-axial rays Allow MP2 only for axial ray diagram 2 AO1

Both focal points labelled with common focus closer to Condone missing arrows

eyepiece lens

Condone missing construction line

Treat ‘focal length’ as neutral.

Insist that focal points are common and on

principal axis.

02.2 The mark scheme gives some guidance as to what Relative brightness (partial 1/2; full 2/2) 6 2 × AO1

statements are expected to be seen in a 1- or 2- 1. (Image formed by) B brighter than A (because

mark (L1), 3- or 4- mark (L2) and 5- or 6- mark (L3) B larger diameter than A) B has a greater 3 × AO2

or

answer. Guidance provided in section 3.10 of the collecting power than A 1 × AO3

‘Mark Scheme Instructions’ document should be 2. Collecting power B = 2.25 × collecting power A

used to assist in marking this question. Show features (partial 1/ first 3; full = partial +

2/last 3)

Mark Criteria 1. (angular) resolution of B > A or Resolution of

All three areas covered in some detail. B = 1.5 × A

6 −5

6 marks can be awarded even if there is an 2. Angular size of Mars = 8.2 × 10 rad

error and/or parts of one aspect missing. allow −5 from radius

[ 4.1 × 10 rad ]

A fair attempt to analyse all three areas. If 3. Magnified A = 25 × 8.2 × 10−5

8 there are several errors or missing parts = 2.1 × 10−3 rad and Magnified B

then 5 marks should be awarded. = 40 × 8.2 × 10−5 = 3.3 × 10−3 rad

Two areas successfully discussed, or one or minimum angle resolvable with the eye

4 −5

discussed and two others covered using this telescope: A = 1.2 × 10 rad and B

partially. Whilst there will be gaps, there = −6

7.5 × 10 rad

should only be an occasional error. 4. Both better than resolution of eye

One area discussed and one discussed 5. A can resolve separation 990 km (15%

partially, or all three covered diameter of Mars) or B can resolve 620 km

partially. There are likely to be several (9% diameter of Mars)

errors and omissions in the discussion. 6. Images in B appear 1.6 × larger than A

2 Only one area discussed or makes a partial Aberrations (partial 1/3; full 3/3)

attempt at two areas. 1. (Dispersion due to lenses so) A shows (more)

chromatic aberration

1 None of the three areas covered without

2. Idea that the use of a parabolic mirror

significant error.

produces no spherical aberration with B

3. B better than A for aberrations.

If no other marks given: award MAX 1 for two

02.3 Two from: Max 2 AO1

Better quantum efficiency and therefore more (of the features / two advantages without explanation

•

incident) light/photons detected (per second)

• Pixels smaller than rods/cones/retinal cells therefore better

resolution

• Detects light outside visible spectrum so more information /

more (of the incident) light detected with CCD

• Longer exposure (time) possible so more light/photons

detected

Total 10

How to answer it

Astrophysics: Telescopes, Aberrations & CCDs

What this question tests

This 10-mark examination question tests fundamental core principles from the Astrophysics option module:

  • Accurate construction of a ray diagram for an astronomical refracting telescope in normal adjustment using three non-axial rays and a common focal plane.
  • Extended multi-step comparison between a refracting and reflecting telescope across three essential criteria: collecting power / relative brightness, angular resolution and detail (subtended angles vs. human eye limits), and optical aberrations (chromatic vs. spherical).
  • Advantages of Charge-Coupled Devices (CCDs) over the human eye in modern astronomical imaging, requiring full physical mechanisms rather than simple bullet points.
Question 02.1 • 2 Marks

Astronomical Refractor Ray Diagram in Normal Adjustment

Three non-axial rays and coincident focal points

💡 Key Knowledge

  • Normal adjustment means the image is formed at infinity. Hence, the principal focal plane of the objective ( Fₒ ) and eyepiece ( Fₑ ) coincide.
  • The focal length of the objective lens is significantly longer than that of the eyepiece lens ( fₒ > fₑ ).
  • Non-axial rays enter parallel to each other but at an inclined angle to the principal axis.

✅ What the Diagram Must Show

Ray Path Construction:
  1. Draw 3 parallel rays entering the objective lens at an angle to the principal axis.
  2. The central ray passes straight through the optical centre of the objective undeflected.
  3. All 3 rays converge at an intermediate real focal point on the shared focal plane ( Fₒ, Fₑ ) located closer to the eyepiece.
  4. The rays continue to the eyepiece lens and emerge parallel to each other (and parallel to a construction line passing from the intermediate focal point through the centre of the eyepiece).

🧠 Exam Technique & Mark Breakdown

  • Mark 1 (AO1): Diagram correct with a set of three non-axial rays (converging at focal plane, emerging parallel from eyepiece).
  • Mark 2 (AO1): Both focal points labelled with a common focus closer to the eyepiece lens than to the objective lens. Both labels ( Fₒ and Fₑ ) must lie on the principal axis.

❌ Common Errors

  • Drawing rays parallel to the principal axis (axial rays)—this immediately disqualifies Mark 1.
  • Drawing only two rays instead of the specified three rays.
  • Placing the intermediate focus midway or closer to the objective lens instead of closer to the eyepiece.
  • Rays not emerging parallel from the eyepiece lens.
Examiner Guidance: Condoned: missing arrows, missing construction lines. Strict rule: Focal points must be coincident (common) and lie directly on the principal axis.
Question 02.2 • 6 Marks (Level of Response)

Comparative Analysis: Refractor A vs. Reflector B

Brightness, detail (resolving power), and aberrations when observing Mars

📐 Step-by-Step Quantitative Analysis

1. Collecting Power & Brightness:
Collecting power is proportional to diameter squared ( Collecting Power ∝ D² ).
Ratio: (D_B / D_A)² = (0.18 / 0.12)² = (1.5)² = 2.25 .
→ Image in telescope B is 2.25 times brighter than in A (or collects 2.25× more light).
2. Mars Angular Size Subtended at Earth:
Convert astronomical units to metres: 1 AU ≈ 1.50 × 10¹¹ m .
Distance to Mars d = 0.55 × 1.50 × 10¹¹ m = 8.25 × 10¹⁰ m .
Diameter of Mars s = 6.8 × 10⁶ m .
Angle subtended at Earth: θ = s / d = (6.8 × 10⁶) / (8.25 × 10¹⁰) ≈ 8.24 × 10⁻⁵ rad .
3. Magnified Angular Size vs. Eye Resolution:
Using angular magnification M = θ_image / θ_object :
• With A ( M = 25 ): θ_image = 25 × 8.24 × 10⁻⁵ = 2.1 × 10⁻³ rad .
• With B ( M = 40 ): θ_image = 40 × 8.24 × 10⁻⁵ = 3.3 × 10⁻³ rad .
Both magnified angles exceed the eye's angular resolution limit ( ~3 × 10⁻⁴ rad ), so Mars will be clearly seen as an extended disc (not a point source) with both telescopes. Furthermore, telescope B magnifies the image 1.6× larger than A ( 40 / 25 = 1.6 ).
4. Resolving Detail (Diffraction Limit):
Rayleigh criterion minimum resolvable angle: θ ≈ λ / D .
Since D_B (0.18 m) > D_A (0.12 m) , telescope B has a smaller minimum resolvable angle by a factor of 0.18 / 0.12 = 1.5 .
Telescope B has superior resolving power and can resolve much finer features on Mars's surface.

✅ Key Points to Cover for Level 3 (5–6 Marks)

  • Relative Brightness: B produces a brighter image than A because B has a larger diameter (collecting power is 2.25× greater).
  • Features & Resolution: B reveals finer surface detail than A because of its larger aperture (smaller diffraction limit / resolution of B is 1.5× better). Mars subtends an unmagnified angle of ~ 8.2 × 10⁻⁵ rad ; when magnified, both exceed the naked-eye limit ( 3 × 10⁻⁴ rad ), but B provides 1.6× greater magnification.
  • Aberrations: Refractor A suffers from chromatic aberration (different wavelengths refract by different amounts through glass lenses) and potentially spherical aberration if not parabolic. Reflector B uses mirrors, completely eliminating chromatic aberration, and a parabolic primary mirror avoids spherical aberration. Overall, B gives superior optical quality.

❌ Common Errors & Pitfalls

  • Stating brightness is directly proportional to diameter instead of diameter squared ( D² ).
  • Forgetting to convert AU to metres when calculating the angular size of Mars.
  • Claiming reflectors suffer from chromatic aberration (mirrors reflect all wavelengths identically!).
  • Vague qualitative statements without using data from Table 1 or the constants provided.
Examiner Insight (Level of Response Breakdown):
• Level 3 (5–6 marks): All three aspects (brightness, features/resolution, aberrations) discussed with accurate supporting quantitative calculations.
• Level 2 (3–4 marks): Two areas successfully evaluated, or one fully and two partially.
• Level 1 (1–2 marks): Only one area properly addressed or fragmented notes.
Question 02.3 • 2 Marks

Advantages of a CCD over the Human Eye

Beyond simple digital data storage and computer processing

✅ Accepted Advantages (State & Explain)

Choose any two complete explanations:

  • Higher Quantum Efficiency: A CCD has a much higher quantum efficiency (~80% vs ~1–2% for the human eye), meaning a much higher percentage of incident photons are detected.
  • Higher Spatial Resolution: The pixels in a CCD are smaller than the rods/cones/retinal cells of the human eye, allowing finer detail to be resolved.
  • Broader Spectral Range: CCDs detect wavelengths outside the visible spectrum (such as UV and IR), providing wider astronomical data.
  • Longer Exposure Integration: CCDs can collect light over long integration times (long exposures), allowing extremely faint astronomical objects to become clearly visible.

🧠 Exam Technique: Securing Both Marks

Marking rule: Both marks are for explained advantages.
If you only list features without explaining their effect (e.g. just writing "higher quantum efficiency" and "smaller pixels"), the mark scheme caps you at 1 mark maximum for two unelaborated points!

Always use the structure: Feature + Consequence for observation.

Topics

Optional topics · 3.9 Astrophysics (A-level only)

Question and mark scheme from the AQA A-Level Physics examination, Paper 3 (3BA), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.