(a) Draw the ray diagram to show the image formation by a refracting telescope and write the expression for angular magnification for the telescope in normal adjustment.
(b) Give two reasons to explain why a reflecting telescope is preferred over a refracting telescope.
(a) Draw the ray diagram to show the image formation by a refracting telescope and write the expression for angular magnification for the telescope in normal adjustment.
(b) Give two reasons to explain why a reflecting telescope is preferred over a refracting telescope.
(a) Ray diagram (astronomical refracting telescope, normal adjustment):
- The objective (large focal length f_o, large aperture) forms a real, inverted image A'B' of a distant object at its focus.
- In normal adjustment, this image lies at the focus of the eyepiece (small focal length f_e) as well, so the final image forms at infinity and the eye views it relaxed.
- Parallel rays from the distant object → objective → real inverted image at common focus → eyepiece → parallel emergent rays to the eye.
Angular magnification (normal adjustment):
(magnitude ; the minus sign shows the final image is inverted). The tube length .
(b) Two reasons a reflecting telescope is preferred:
- No chromatic aberration — a mirror reflects all wavelengths identically, whereas a lens objective disperses colours and blurs the image.
- Larger aperture / brighter, higher-resolution image — a large concave mirror can be made and supported from behind cheaply, gathering far more light; large lenses sag under their own weight and suffer spherical aberration.
Marking Scheme
- 11.5 marks: correct labelled ray diagram of the refracting telescope (objective forming real inverted image at the common focus, eyepiece giving final image at infinity in normal adjustment).
- 20.5 mark: correct expression (or magnitude ) for normal adjustment.
- 31 mark: any two valid reasons for preferring a reflecting telescope (no chromatic aberration; larger aperture/brighter image; no spherical aberration with a parabolic mirror; cheaper/easier to support a large mirror) — 0.5 mark each.
Hint
In normal adjustment (image at infinity). For part (b) think chromatic aberration and aperture/light-gathering.
Quick Oral Answer
A refracting telescope's objective forms a real inverted image of a distant object at its focus, which the eyepiece then magnifies with the final image at infinity in normal adjustment, giving magnification ; reflecting telescopes are preferred because a mirror has no chromatic aberration and can be made with a much larger aperture for brighter, sharper images.
Analysis & Explanation
Concept: A refracting telescope uses two converging lenses — a long-focal-length objective and a short-focal-length eyepiece. Its job is angular magnification: it makes a distant object subtend a larger angle at the eye, not to magnify size on a screen.
Normal adjustment: This is the relaxed-eye setting where the final image is at infinity; the intermediate real image sits exactly at the common focus of objective and eyepiece, giving . To maximise magnification you want a long fo and short fe.
Exam trap: Students confuse the microscope (both short focal lengths, image at least distance of distinct vision) with the telescope (long objective focal length, image at infinity in normal adjustment). Always label the common focal point and mark the inverted intermediate image.
Real-world: All the largest modern telescopes (Hubble, the 10 m Keck, the upcoming ELT) are reflectors precisely for the two reasons above — mirrors avoid chromatic aberration and can be built enormous, which is why professional astronomy abandoned giant refractors over a century ago.
Common Mistakes
- 1Writing the microscope magnification or drawing both lenses with short focal lengths — a telescope needs a long-focal-length objective.
- 2Forgetting to state 'normal adjustment' means the final image is at infinity with the intermediate image at the common focus.
- 3Giving vague reasons like 'reflecting telescope is better' without naming the specific defects (chromatic/spherical aberration) or the aperture advantage.
Interesting Facts
Isaac Newton built the first reflecting telescope in 1668 specifically to defeat the chromatic aberration that plagued the refractors of his day.
The largest refracting telescope ever built, the 1897 Yerkes Observatory refractor, has a 40-inch (1.02 m) lens — no bigger refractor has been made since, because larger lenses sag under gravity.
The Hubble Space Telescope's primary mirror is 2.4 m across, and the Extremely Large Telescope under construction in Chile uses a segmented mirror 39 m in diameter — all reflectors.
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Frequently Asked Questions
What is meant by 'normal adjustment' of a telescope?
Normal adjustment is the setting in which the final image is formed at infinity, so the eye views it in its most relaxed state. The real, inverted image made by the objective falls exactly at the focus of the eyepiece, and the magnification is .
Why is the objective of a telescope large and of long focal length?
A large aperture gathers more light, giving a brighter image and better resolving power of distant faint objects. A long objective focal length combined with a short eyepiece focal length maximises the angular magnification .
What are the two main aberrations a reflecting telescope avoids?
A mirror objective avoids chromatic aberration entirely because reflection is wavelength-independent. Using a parabolic mirror also removes spherical aberration, giving a sharp image that a spherical lens objective cannot match.