The compound microscope

The compound microscope (Figure 1) uses several lenses to produce a highly magnified image of an object.


The diagram shows the microscope in normal adjustment, that is, with the final image at the near point (25 cm from the eye) (distance D from the eye lens). This setting gives the maximum angular size of image without eye strain.

The objective lens produces a real, inverted image of the object 0 at I₁ This is then viewed by the eye lens and this gives a final virtual image at I. The magnifying power M of the instrument is given by the formula:


where f_e is the focal length of the eye lens, f_o that of the objective lens and v the distance of I₁ from the objective lens.

Therefore you can see that the smaller the focal lengths of the objective and eye lens, the greater is the magnifying power. If the focal length of the objective is too small, however, the object will subtend too great an angle with it and the image will be distorted due to off-axis rays. This is the reason for using the oil immersion objective to reduce the amount of refraction at the first lens surface.


The resolving power of a microscope can be shown to depend on the wavelength of light used (l), the refractive index of the medium above the slide (n) and the angle subtended at the objective (a) (Figure 2):

An alternative and very useful formula for the magnifying power M of a compound microscope is:


where m_o and m_e are the magnifications of the objective lens and eyepiece lens respectively.