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Compound Microscope

The magnifying power of a simple microscope can be increased by decreasing the focal length of the lens as M = 1 + D/ƒ.

But due to constitutional difficulties, the focal length of a lens cannot be decreased beyond a certain limit. Moreover, the lens of small focal length has a small diameter because the curvature of the surface is large and the field of view is small.

Therefore, to increase the magnifying power, two separate lenses are used. The lens near the object is called the objective and the other which is nearer the eye is known as the eyepiece. The objective and the eyepiece are both convex lenses. The objective is of small diameter and small focal length (high power) whereas the eyepiece is of large focal length than the objective.

The object AB is placed at a distance slightly greater than the focal length of the objective. An inverted image A’B’ is formed at A’. The eyepiece is adjusted so that the distance of A’ from it is less than its focal length. As the eyepiece acts as a simple magnifying glass, the final image PQ is formed at P which is magnified and virtual.

Magnifying power: When the microscope is in normal use, the final image PQ is formed at the near point at a distance D from the eye.

∴ M = M_e × M_o

As the eyepiece acts as a simple magnifying glass, its magnifying power

where ƒ_e is the focal length of the eyepiece.

If the distance of the image A’B’ from the objective = v and the distance of the object AB from the objective = u

Then, Me = v/u

In the case of most of the microscopes the distance between the objective and eyepiece is fixed. The lenses are fixed at the two ends of a tube. Then the microscope is focused by moving it bodily either towards the object or away from the object.

Therefore, in the relation for the magnifying power,

It is necessary to find v in terms of ƒ₀, ƒ_e and the distance between the objective and the eyepiece.

Suppose, the distance between the objective and the eyepiece,

= OE = L,

OA’ = v, ∴ v = OE – A’E

v = L – A’E

As A’ acts as a point object for the eyepiece whose image is formed at P,

Substituting the value of v in the formula for magnifying power,

From equation (iii), knowing ƒ₀, ƒ_e, D and L, the magnifying power of the microscope can be calculated.

Note: Actually the objective is not a single lens but it consists of one or more achromatic lenses and the eyepiece also consists of two lenses which give an optically true image. The above discussion only gives the simplest case where O represents the centre of the lens which is equivalent to the lenses present in the objective while E represents the centre of the lens which is equivalent to the lenses present in the eyepiece.