A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Image Formation and Angular Magnification in a Telescope — mark scheme explained
The short answer
In this section, we will explore the principles of image formation and angular magnification in a telescope when it is used in normal adjustment. Understanding these concepts is crucial for grasping how telescopes work and how they enhance our ability to observe distant objects.
The question
A telescope has an objective lens with a focal length of 120 cm and an eyepiece with a focal length of 5 cm. Calculate the angular magnification of the telescope.
[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 include units. For explanations, use clear and concise language. For diagrams, label all components accurately.
What the command words demand
- Calculate
- Perform a numerical calculation to find the answer.
- Explain
- Provide a clear and concise explanation of a concept or process.
- Draw
- Create a diagram or graph to illustrate a point.
- Identify
- Recognize and name specific components or values in a problem.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate 5-7 minutes for questions on this topic to ensure you have enough time to draw accurate ray diagrams and perform necessary calculations.
- Identify the given values: f o = 120 cm, f e = 5 cm.0 marks
- Use the formula for angular magnification: M = f o / f e .1 mark
- Substitute the values into the formula: M = 120 cm / 5 cm .1 mark
- Calculate the result: M = 24 .1 mark
Final answer: The angular magnification of the telescope is 24.
Work through every step correctly and you earn all 3 marks.
Another worked example
A star subtends an angle of 0.1° at the unaided eye. If a telescope with an objective lens focal length of 150 cm and an eyepiece focal length of 6 cm is used, what is the angle subtended by the image at the eye?
- Identify the given values: θ object = 0.1°, f o = 150 cm, f e = 6 cm.0 marks
- Calculate the angular magnification using the formula: M = f o / f e .1 mark
- Substitute the values into the formula: M = 150 cm / 6 cm .0 marks
- Calculate the result: M = 25 .1 mark
- Use the magnification to find the angle subtended by the image at the eye: θ image = M × θ object .1 mark
- Substitute the values into the formula: θ image = 25 × 0.1° .0 marks
- Calculate the result: θ image = 2.5° .1 mark
Final answer: The angle subtended by the image at the eye is 2.5°.
Work through every step correctly and you earn all 4 marks.
Common mistakes
Confusing the focal lengths of the objective lens and the eyepiece
Why it happens: Students may mix up which focal length belongs to which lens, leading to incorrect calculations.
Fix: Always label the focal lengths clearly: f o for the objective lens and f e for the eyepiece.
Using the wrong formula for angular magnification
Why it happens: Students might use a different formula or mix up the terms in the correct formula.
Fix: Memorize and practice using the correct formula: M = f o / f e .
Forgetting to convert angles to radians when necessary
Why it happens: Students may forget that some calculations require angles in radians, especially when using trigonometric functions.
Fix: Always check if the problem requires angles in degrees or radians and convert accordingly.
Not understanding the concept of normal adjustment
Why it happens: Students may not grasp why the final image must be at infinity for optimal viewing.
Fix: Review the definition and importance of normal adjustment in telescopes.
Incorrectly drawing ray diagrams
Why it happens: Students may draw rays incorrectly, leading to an incorrect image formation.
Fix: Practice drawing ray diagrams step-by-step and ensure that the rays from the object intersect at the correct points.
Misinterpreting the angle subtended by the image
Why it happens: Students may confuse the angle subtended by the image with other angles in the problem.
Fix: Clearly identify and label all angles in the problem, especially θ image and θ object .
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 |
|---|---|---|
| Angular Magnification | Calculate a telescope's angular magnification from the objective and eyepiece focal lengths. | 3 |
| Telescope Angular Magnification | Find the image angle using the telescope's angular magnification from the two focal lengths. | 4 |
| Telescope Magnification | Rearrange the angular magnification formula to find the objective lens focal length. | 3 |
| Angular Magnification Calculation | Rearrange the angular magnification formula to find the angle subtended by the object. | 3 |
| Total across these question types | 13 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.