Practise › Questions › Telescopes and image formation
Telescopes and image formation questions
A refracting telescope is two converging lenses sharing a focal point, and the ratio of their focal lengths gives the angular magnification. Reflecting telescopes do the same job with a mirror, which avoids chromatic aberration and folds a long focal length into a short tube.
20 original questions · 60 marks · the telescopes and image formation notes · Astrophysics
On this topic the library is tagged for AQA.
Every question here is written for this library rather than taken from a past paper. Write your answer out before opening a mark scheme: the schemes award marks point by point, and the marks are easier to see when you have something of your own to compare against.
State what is meant by a refracting telescope in normal adjustment, and where the final image is formed.
Mark scheme
The focal planes of the objective and the eye lens coincide (1). The final image is formed at infinity, viewed by a relaxed eye (1).Define the angular magnification of an astronomical telescope.
Mark scheme
The angle subtended at the eye by the final image divided by the angle subtended at the unaided eye by the object (1). It is a ratio of angles, not of sizes (1).Name the two mirrors of a Cassegrain reflecting telescope, giving the shape of each, and state where the light comes to its final focus.
Mark scheme
A concave parabolic primary mirror and a convex secondary mirror (1). The secondary reflects the converging light back through a central hole in the primary, to a focus just behind it (1).Explain why the angular magnification of a telescope has no unit.
Mark scheme
It is the ratio of two angles: the angle subtended at the eye by the final image divided by the angle subtended by the object at the unaided eye (1). Both angles carry the same unit, which cancels in the ratio (1).A refracting telescope is pointed at a distant star. State where the objective lens forms an image of the star, and the nature of that image.
Mark scheme
In the objective's focal plane, one focal length behind the lens, because the light arrives as (near-)parallel rays (1). The image is real (and inverted) (1).A telescope in normal adjustment has its eye lens replaced by one of half the focal length. State the effect on the angular magnification.
Mark scheme
M = fo/fe, so halving fe doubles the angular magnification (1).A refractor has an objective of focal length 1.5 m and an eye lens of focal length 30 mm. For normal adjustment, calculate the angular magnification and the length of the telescope.
Mark scheme
M = fo/fe = 1.5/0.030 (1)
M = 50 (1)
Length = fo + fe = 1.53 m (1)The Moon subtends an angle of 9.0 × 10−3 rad to the naked eye. Calculate the angle it subtends through a telescope with a 1.0 m objective and a 25 mm eye lens in normal adjustment.
Mark scheme
M = fo/fe = 1.0/0.025 = 40 (1)
Angle through the telescope = 40 × 9.0 × 10−3 (1)
= 0.36 rad (1)A refractor in normal adjustment has an angular magnification of 60 and a tube 1.22 m long. Calculate both focal lengths.
Explain what causes chromatic aberration in a refracting telescope, and why a reflecting telescope does not suffer from it.
Explain what is meant by spherical aberration, and how the design of the Cassegrain primary mirror avoids it.
Two stars are separated by an angle of 1.5 × 10−4 rad when viewed with the unaided eye. Through a refractor in normal adjustment fitted with a 20 mm eye lens, they appear separated by 6.0 × 10−3 rad. Calculate the focal length of the objective.
An astronomer removes the eyepiece of a refractor and places a CCD in the focal plane of the objective, which has a focal length of 1.4 m. Mars subtends an angle of 1.2 × 10−4 rad to the naked eye. The pixels of the CCD are 5.0 μm wide. Determine the number of pixels spanned by the diameter of the image of Mars.
Explain how the Cassegrain design gives a long effective focal length in a short tube, and give one practical benefit of the short tube.
A refractor in normal adjustment has an objective of focal length 1.25 m in a tube 1.30 m long. Show that its angular magnification is about 25. Go on to calculate the angle subtended through the telescope by a lunar crater that subtends 6.0 × 10−5 rad to the naked eye.
A Cassegrain telescope has an effective focal length of 3.2 m and is used with an 8.0 mm eyepiece. A lunar crater subtends 4.0 × 10−5 rad to the naked eye. Calculate the magnification and the angle the crater subtends through the telescope.
A school is choosing between a large refractor and a Cassegrain reflector of the same aperture. Give two advantages of the reflector and one practical advantage of the refractor.
A magazine advert praises a small telescope for its “500× magnification”. Explain why this figure alone says little about the telescope's quality.
A catalogue states that a refractor gives an angular magnification of 60 in normal adjustment with the 25 mm eyepiece supplied, in a tube 1.05 m long. Deduce whether the claim is consistent with the stated dimensions.
A refractor in normal adjustment is pointed at a distant star cluster. Explain fully how the two lenses produce the final image, and show how the angular magnification is related to the two focal lengths.
The same practice on paper: the printable workbook for this topic, questions and a worked answer book.
Practise telescopes and image formation one question at a time
The player marks nothing for you. It shows one question, waits, then shows the scheme so you can mark yourself, and brings a question back sooner when it went badly.