The power and aperture of lenses \( L_1, L_2 \) and \( L_3 \) are given below in tabular format. Which pair of lenses should be chosen for constructing a microscope?
| Lens | Power | Aperture |
| \( L_1 \) | 3 D | 8 cm |
| \( L_2 \) | 6 D | 1 cm |
| \( L_3 \) | 10 D | 1 cm |
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( L_2 \) as eyepiece and \( L_3 \) as objective
In a compound microscope both lenses should have short focal lengths, and the objective should have the shortest focal length (highest power) and a small aperture, since the object is placed just beyond its focus. The eyepiece has a somewhat larger focal length.
\( f_1 = 1/3\,\mathrm{m} \approx 33\,\mathrm{cm} \)
\( f_2 = 1/6\,\mathrm{m} \approx 17\,\mathrm{cm} \)
\( f_3 = 1/10\,\mathrm{m} = 10\,\mathrm{cm} \)
\( L_3 \) has the highest power and a small aperture, so it is the objective; \( L_2 \), the next most powerful, is the eyepiece.
Why the other options are incorrect
Option (2) \( L_3 \) as eyepiece and \( L_2 \) as objective — Incorrect. This swaps the two lenses; the objective must be the one with the shorter focal length, \( L_3 \).
Option (3) \( L_2 \) as eyepiece and \( L_1 \) as objective — Incorrect. \( L_1 \) has the lowest power and a large aperture, which suits the objective of a telescope, not of a microscope.
Option (4) \( L_1 \) as eyepiece and \( L_2 \) as objective — Incorrect. \( L_1 \) is the weakest lens, and \( L_2 \) is not the most powerful one, so neither is in its right place.