A simple magnifier or microscope is a converging lens of small focal length (Fig.). In order to use such a lens as a microscope, the lens is held near the object, one focal length away or less, and the eye is positioned close to the lens on the other side. The idea is to get an erect, magnified and virtual image of the object at a distance so that it can be viewed comfortably, i.e., at 25 cm or more.
If the object is at a distance f, the image is at infinity. However, if the object is at a distance slightly less than the focal length of the lens, the image is virtual and closer than infinity. Although the closest comfortable distance for viewing the image is when it is at the near point (distance D = 25 cm), it causes some strain on the eye. Therefore, the image formed at infinity is often considered most suitable for viewing by the relaxed eye.
Ray diagram for image formation :
The linear magnification m, for the image formed at the near point D, by a simple microscope can be obtained by using the relation
Now according to sign convention, v is negative, and is equal in magnitude to D. Thus, the magnification is
The angle subtended at the eye by the image when the object is at u is called angular magnification.
The angular magnification
