Find the maximum magnifying power of a compound microscope having a 25 dioptre lens as the objective, a 5 dioptre lens as the eyepiece and the separation 30 cm between the two lenses. The least distance form clear vision is 25 cm.

Question

Philoid · Accepted Answer

Given data

Least distance of clear vision, D = 25 cm

Separation between the objective and the eyepiece, L = 30 cm

Magnifying power is maximum when the image is formed by the eyepiece at the least distance of clear vision which is 25cm for normal eye.

For eyepiece-

Power of the eyepiece = 5 D

The focal length of the eyepiece is given by

So, and

Using lens formula, for eyepiece

For Objective lens-

Power of the objective lens = 25 D

The focal length of the objective lens can be calculated using-

Let L be the length of the compound microscope and be the object distance and be the

image distance for the objective lens.

So, the image distance for the objective lens will be-

Since the image formed is real and inverted, the value of

Using lens formula

cm

Now, to calculate maximum magnifying power of the compound microscope, we use,

Hence, the maximum magnifying power of the compound microscope is 8.3831