The purpose of the microscope is to produce magnified images of small objects. Such an image is produced by an optical system that consists of an objective and an eyepiece (also known as theocular). An objective consists of a lens with a short focal length. The object of observation is placed beside the objective at a distance s > f1 near the first focus. The objective produces a magnified inverted image, available for observation through the eyepiece, which consists of a converging lens with a short focal length.
When analyzing the path of the rays, remember that the eye generally accommodates to the distance of normal vision: d0 = 25 cm. The viewer can look at a small object directly putting it at a distance d0 from the eye, or through a microscope, examining the virtual image of the object, as produced by the eyepiece, from the same distance d0. The ratio of the angle that is subtended at the eye by the final image to the angle subtended at the unaided eye by the object is called the angular magnification. Since in both cases the object is viewed from the same distance d0, the angular magnification also coincides with the lateral magnification of a system of two lenses.
The virtual image of an object observed through the eyepiece is always inverted. If this is inconvenient for any reason, the object itself can be inverted. Note that the magnification of the microscope is always characterized as a positive value.
The magnification M is determined as the product of the magnifications of the objective and the eyepiece. In the case when f1 and f2 are much smaller than the distance Δ between them, the microscope's magnification is expressed by the formula
M = (d0Δ)/(f1f2) .
The standard microscope has Δ = 160 mm.
An optical microscope can magnify objects by several hundreds of times. At particularly large magnification, diffraction phenomena appear.