Four double convex lenses, with the following specifications are available.
| Lens | Focal length | Aperture |
|---|---|---|
| A | 100 cm | 10 cm |
| B | 100 cm | 5 cm |
| C | 10 cm | 2 cm |
| D | 5 cm | 2 cm |
Which two of the given four lenses should be selected as the objective and eye-piece to construct an astronomical telescope?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Lenses A and D respectively
For an astronomical telescope the angular magnification in normal adjustment is \( m = f_o/f_e \), so the objective should have a large focal length and the eyepiece a small focal length. The objective should also have a large aperture to collect more light and give a brighter image.
The objective is the lens with \( f = 100\,\mathrm{cm} \) and the larger aperture of 10 cm, which is A. The eyepiece is the lens with the smallest focal length, which is D (\( f = 5\,\mathrm{cm} \)).
\( \displaystyle m = \frac{f_o}{f_e} = \frac{100\,\mathrm{cm}}{5\,\mathrm{cm}} = 20 \)
The other pairs give a lower magnification (A and C give 10) or a smaller aperture for the objective (B).
NCERT (2026-27):
Telescope – “… The telescope is used to provide angular magnification of distant objects (Fig. 9.25). It also has an objective and an eyepiece. But here, the objective has a large focal length and a much larger aperture than the eyepiece.”