Simple Microscope

When a convex lens of short focal length is used to see magnified image of a small object, it is called a simple microscope.

When an object is placed between the optical center and the focus of a convex lens, its image is virtual, erect, and magnified and on the same side as the object. Such a lens is held close to eye and the distance of the object is adjusted till a clear image is formed at the least distance of distinct vision.

Magnifying power of a simple microscope

Magnifying power of an optical instrument is the ratio of the angle subtended by the image at the eye to the angle subtended by the object seen directly, when both lie at the least distance of distinct vision or the near point. It is also called angular magnification and is denoted by M.

M = β/α

The angles α and β are small. So, you can replace these by their tangents.

M = (tan β)/(tan α)

tan β = A'B'/A'O = A'B'/D

tan α = A'B''/A'O = AB/D

M = A'B'/AB = A'O/AO (Since triangles are similar)

A'O = –D

AO = –u

M = D/u

If f is the focal length of the lens acting as a simple microscope, then using the lens formula 

v = –D

u = – u

(1/–D) – (1/–u) = (1/f)

(–1/D) + (1/u) = 1/f

D/u = 1 + D/f

M = 1 + D/f

Lesser the focal length of the convex lens, greater is the value of the angular or magnifying power of the simple microscope.

Normal Adjustment

In this case, the image is formed at infinity. The magnifying power of the microscope is defined as the ratio of the angle subtended by the image at the eye to the angle subtended by the object at the unaided eye when the object is placed at D.