Compound Microscope

A compound microscope is an optical instrument used to produce much greater magnification than that produced by simple microscope. The main features of a compound microscope includes two short-focus convex lenses, the objective lens, and the eyepiece.

Demonstration

The most commonly used microscope for general purposes is the standard compound microscope. It magnifies the size of the object by a complex system of lens arrangement.

It has a series of two lenses;

(i) The objective lens close to the object to be observed

(ii) The ocular lens or eyepiece, through which the image is viewed by eye. Light from a light source (mirror or electric lamp) passes through a thin transparent object.

The objective lens produces a magnified 'real image' (first image of the object). This image is again magnified by the ocular lens (eyepiece) to obtain a magnified 'virtual image' (final image), which can be seen by eye through the eyepiece.

Magnification of a compound microscope: This is the ratio of the image distance produced by a compound microscope to the object distance. The magnification produced by objective lens is $v/u$.

Where

$V$ is the image distance

$U$ is the object distance

The magnification given by the eyepiece is given by;

$M_e = \frac{25}{f_e} + 1$

If the final image is formed at the least distance of distinct vision ($V = 25\text{cm}$).

$M_c = M_o \cdot M_e$

Combine eqn (i) and (ii)

Then

$M_c = \left(\frac{v}{u}\right)\left(\frac{25}{f_e} + 1\right)$

The above formula shows that the final virtual image is formed at the least distance of distinct vision.

The uses of a compound microscope includes the following:

1. Used to magnify microorganism such as bacteria, which cannot be seen by naked eyes.
2. Used in hospitals widely to detect microorganisms in specimens provided by patients. A specimen is a small amount that is taken for testing. Blood is an example of specimens. In hospitals, microscopes can detect parasites such as plasmodium ssp (a causative agent for malaria) in blood specimen.

Example 2.

A certain microscope consists of two converging lenses of focal length 10cm and 4cm for the objective and eyepiece, respectively. The two lenses are separated by a distance of 30cm. The instrument is focused so that the final image is at infinity. Calculate the position of the object and the magnification of the objective lens. For the objective lens

$\frac{1}{U} + \frac{1}{V} = \frac{1}{F_o}$

Where

$F_o = 10\text{cm}$

The objective lens forms a real image of the object at the principal focus of the eyepiece.

Thus

$V = (30 - 4)$

$= 26\text{cm}$

Thus $\frac{1}{U} + \frac{1}{V} = \frac{1}{10}$

$\frac{1}{U} + \frac{1}{26} = \frac{1}{10}$

$\frac{1}{U} = \left(\frac{1}{10} - \frac{1}{26}\right)$

$\left(\frac{1}{U}\right)^{-1} = \left(\frac{4}{65}\right)$

$\left(\frac{1}{U}\right)^{-1} = \left(\frac{4}{65}\right)^{-1}$

$U = \left(\frac{65}{4}\right)$

The distance of object, $U = 16.25\text{cm}$

The magnification given by the objective lense is given by:

Whereas:

$V = 26\text{cm}$

$U = 16.25\text{cm}$

$M_o = \left(\frac{26\text{cm}}{16.25\text{cm}}\right)$

The magnificent given by objective lens, $M_o = 1.6$.