Astronomical telescope consisting of two converging lenses (A-level only) — AQA A-Level Physics

This topic covers the optical arrangement and function of a simple astronomical telescope made from two converging lenses. You will learn how the objective lens and eyepiece work together to produce a magnified image of distant objects, and how to calculate the angular magnification and lens separation in normal adjustment.

Understanding this telescope is essential for A-level physics as it applies the principles of refraction, lens formulae, and ray diagrams to a practical instrument. It also appears frequently in exams, testing your ability to draw ray diagrams, perform calculations, and explain image formation.

• →The objective lens has a long focal length and forms a real, inverted, diminished image of a distant object at its focal plane.
• →The eyepiece has a short focal length and acts as a magnifying glass, producing a virtual, inverted final image at infinity in normal adjustment.
• →Angular magnification M = fo / fe, where fo is the focal length of the objective and fe is the focal length of the eyepiece.
• →In normal adjustment, the separation between the lenses is d = fo + fe, and the final image is at infinity.
• →The final image is inverted, which is acceptable for astronomical observations but not for terrestrial use.

• Draws two converging lenses on a common principal axis with the objective of longer focal length than the eyepiece.
• Shows non-axial parallel rays from a distant object incident on the objective lens.
• Locates the real intermediate image at the focal plane of the objective.
• Places the intermediate image at the principal focus of the eyepiece so emergent rays are parallel.
• Defines angular magnification as the ratio of the angle subtended at the eye by the final image to the angle subtended at the unaided eye by the object, M = β/α.
• States that in normal adjustment the final image is at infinity and the eye is relaxed.
• Explains that the intermediate image is formed at the common principal focus of the objective and eyepiece, so the separation of the two lenses is f₀ + fₑ.
• Derives or applies M = f₀/fₑ for an astronomical telescope in normal adjustment.
• Uses the small-angle approximation tan θ ≈ θ in radians when relating angles to focal lengths.
• Recognises that the final image is inverted and that angular magnification is a dimensionless ratio.

• 💡Use a ruler and draw rays as straight lines with arrowheads showing direction.
• 💡Mark focal points clearly with F or F′ so the examiner can follow your construction.
• 💡Sketch a ray diagram with the intermediate image at the common principal focus and mark the angles α and β clearly before substituting into M = β/α.
• 💡When calculating M, convert all focal lengths to metres first, then divide; the result has no unit.
• 💡If asked to explain normal adjustment, state that the final image is at infinity and the eye is relaxed, then link this to the lens separation f₀ + fₑ.
• 💡Always draw clear ray diagrams with at least two rays from the top of the object: one parallel to the principal axis and one through the optical centre. Label the focal points and indicate the intermediate and final images.
• 💡When calculating magnification, ensure both focal lengths are in the same units and remember that M has no units. For lens separation, use d = fo + fe only in normal adjustment.
• 💡In explanations, use precise terms: 'real', 'virtual', 'inverted', 'diminished', 'magnified', 'principal focus'. Avoid vague language like 'bigger' or 'upside down'.

• Drawing rays from a finite object point on the axis; correction: draw parallel rays entering at an angle to the principal axis.
• Drawing the intermediate image beyond the eyepiece focal point; correct by placing it at the eyepiece principal focus for normal adjustment.
• Showing emergent rays converging or diverging; correct by drawing them parallel to each other.
• Using M = fₑ/f₀ instead of M = f₀/fₑ; correct by checking that a long objective focal length and short eyepiece focal length give a large magnification.
• Treating the lens separation as f₀ − fₑ; correct by recalling that in normal adjustment the intermediate image is at the common focal point, so the separation is f₀ + fₑ.
• Forgetting to convert focal lengths to the same unit before dividing; correct by converting both to metres, for example 1.20 m and 0.030 m.
• Describing the final image as real and inverted; correct by stating that in normal adjustment the final image is virtual, inverted and at infinity.
• Students often think the final image is upright. Correction: The objective lens inverts the image, and the eyepiece does not correct this, so the final image is inverted.
• Students may confuse the roles of the lenses, thinking the eyepiece has a long focal length. Correction: The objective has a long focal length, and the eyepiece has a short focal length to achieve high magnification.
• Students sometimes use M = fe / fo. Correction: Angular magnification is M = fo / fe, which is greater than 1 for a telescope.

1. 1Day 1-2: Review the properties of converging lenses, including focal length, real and virtual images, and ray diagrams. Practice drawing ray diagrams for a single lens.
2. 2Day 3-4: Learn the structure and function of the astronomical telescope. Draw a detailed ray diagram for normal adjustment, labelling all key points and images.
3. 3Day 5-6: Derive and apply the formula for angular magnification M = fo / fe. Solve numerical problems involving magnification and lens separation.
4. 4Day 7-8: Complete past paper questions on this topic. Focus on explanations of image formation and common exam pitfalls.
5. 5Day 9-10: Create flashcards for key terms and formulas. Test yourself on active recall prompts and review any weak areas.

• 📋Ray diagram questions: You may be asked to draw a ray diagram for a telescope in normal adjustment. Ensure you show the objective and eyepiece, the intermediate real image, and the final virtual image at infinity. Use a ruler and label clearly.
• 📋Calculation questions: These often ask for angular magnification or lens separation. Write down the formula, substitute values with units, and give your answer to an appropriate number of significant figures.
• 📋Explanation questions: You may need to explain why the final image is inverted or why the telescope is in normal adjustment. Use precise terminology and refer to the intermediate image.
• 📋Comparison questions: Compare the astronomical telescope with a reflecting telescope or a microscope. Highlight differences in construction and image orientation.