What is simple microscope ? Obtain the equation of magnification for the image formed at normal vision distance.

Explanation

A simple magnifier or microscope is a converging lens of small focal length.
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. An erect, magnified and virtual image of the object at a distance so that is can be viewed comfortably i.e., at 25 cm or more. If the object is at a distance f the image is at infinity.

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.
The linear magnification m for the image formed at the near point D, by a simple microscope.
`m=v/u` ... (1)
But, lens formula,
`1/f=1/v-1/u therefore 1/u=1/v-1/f`
Multiplying by .v. on both sides,
`therefore v/u=v/v-v/f` ... (2)
From equation (1) and (2),
`m=1-v/f` [`because v/u`=magnification m]
But image distance v=-D
`therefore m= 1-(-D)/(f)`
`therefore m= 1+D/f`