The power of some lenses are given below:
A. 2 D
B. −2 D
C. −50 D
D. 100 D
Which lenses are most suitable to construct a compound Microscope with objective lens and Eyepiece, respectively?
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → D and A only
Both lenses of a compound microscope must be converging (positive power), and the objective must have a much shorter focal length than the eyepiece so that it forms a large magnified image. The focal length follows from the power, \( f = \frac{1}{P} \) with f in metres.
\( \mathrm{A}\ (2\,\mathrm{D}):\ f = \frac{1}{2} = 0.5\,\mathrm{m} = 50\,\mathrm{cm} \)
\( \mathrm{B}\ (-2\,\mathrm{D}):\ f = -50\,\mathrm{cm} \) (diverging)
\( \mathrm{C}\ (-50\,\mathrm{D}):\ f = -2\,\mathrm{cm} \) (diverging)
\( \mathrm{D}\ (100\,\mathrm{D}):\ f = \frac{1}{100} = 1\,\mathrm{cm} \)
B and C are diverging lenses and cannot be used. Of the two converging lenses, D (\( f = 1\,\mathrm{cm} \)) is the one with the short focal length, so it is the objective, and A (\( f = 50\,\mathrm{cm} \)) is the eyepiece.