Question

The focal length of the objective of a compound microscope if fo and its distance from the eyepiece is L. The object is placed at a distance u from the objective. For proper working of the instrument,
(a) L < u
(b) L > u
(c) fo < L < 2fo
(d) L > 2fo

Answer 1

For proper working of the instrument, it must be L > 2fo.

• The focal length of the compound microscope is fo and distance from eyepiece is L.

• The image I1 on the left of the eye lens must be obtained for proper functioning of the compound microscope.
• If the image is not obtained, then Image II would not be obtained as it is now.
• The distance between lenses L has to be large for this to happen.
• Thus, for proper working of the instrument it should be  L > 2fo.

Answer 2

The object is placed at a distance u from the objective. For proper working of the instrument it must be (L > u) and (L > 2$f_0$).

Explanation :

The objective lenses of a short focal length, $f_0$, is used in a compound microscope. The focal length of the objective lens is shorter than the ocular focal length. The object is positioned a slightly greater distance than its focal length. The actual, distorted image of the object forms at a distance less than its focal length somewhere in front of the eyepiece. This image serves as its source and the microscope's final picture forms in between duration, L.  

                                                (OR)

For proper compound microscope operation, Image I1 on the left side of the eye lens. Otherwise, the picture that I wouldn't get as it is now. The distance between lenses L has to be large for this to happen.

Hence L>u and  L>2$f_0$.

Thus, the option (b) and (d) is correct.