Question

In a compound microscope the focal length of objective lens
A. Is more than the focal length of the eyepiece lens
B. Is less than the focal length of the eyepiece lens
C. Is equal to the focal length of the eyepiece lens
D. Is two times to focal length of the eyepiece lens

Answer 1

Hint: Recall the relation between the magnification of the compound microscope and the focal length of the objective lens and the focal length eyepiece lens. Check by which adjustments of focal lengths the main objective of the compound microscope i.e. more magnification is fulfilled.

Complete step by step answer:
If the focal length of the objective lens in a compound microscope is more, equal or twice the focal length of the eyepiece lens, the image formed by the compound microscope is not clear.
Therefore, these conditions are not used in a compound microscope.
Hence, the options A, C and D are incorrect.

The compound microscope is used to observe an object which is very small.
For the clear observation of this small object, the focal lengths of the objective lens as well as eyepiece lens. So that the image formed by these two lenses combine is clear.
The magnification of the compound microscopes is directly proportional to the magnifications of the objective lens and eyepiece lens.
The magnifications of the objective lens and eyepiece lens are inversely proportional to their focal lengths.
Hence, to increase the magnification, the focal length of the objective lens and eyepiece lens should be decreased.

But if the focal length of the eyepiece is decreased after a certain limit, the eyepiece undergoes aberration and the image formed by eyepiece does not remain clear
Hence, the focal lengths of objective lens and eyepiece in compound microscopes are decreased for more magnification but the focal length of the eyepiece lens is kept more than the focal length of objective lens.
Therefore, in a compound microscope the focal length of an objective lens is less than the focal length of the eyepiece lens.
Hence, the correct option is B.

So, the correct answer is option (B).

Note:
The students may use the concept that the magnification of objective lens and eyepiece lens is inversely proportional to their focal lengths. But the students should also note about the effects when the focal length of the eyepiece lens is decreased beyond a certain limit. One should not derive a conclusion without knowing about the disadvantages of decreasing the focal length of eyepiece.