We seek, with this experiment, to become conversant with simple converging lenses and the familiar compound systems, the microscope and the telescope. We wish that the concepts which underly our understanding would come into focus. These include image, object, and focal lengths, angular and lateral magnification, and so on. All one needs to know is in the text, and we all assume that we have read up on these concepts. Still a few words are in order.
Lenses are``thin" if the thickness of the lens is much less
than the focal length and the object and image distances
used. In that case the Gaussian formula holds:
1o + 1i = 1f.
A lens may be positive or converging, in which case it is
thicker in the middle than at the edges, or negative or
diverging. Positive lenses have positive focal lengths and
vice versa. The focal length of a lens is the distance
from the lens at which parallel light will be focused. A
focal point is a point at which incident parallel light rays are focused.
The power of a lens is defined as the
reciprocal of the focal length measured in meters. The
units of power are meters
or diopters.
An image may be either real or virtual. An image is real if the light rays actually reach the image position without further deviation; in this case the image could, in principle, be shown on a screen. An image is virtual if the image is only apparent and not the effect of the actual convergence of light rays at the image plane. When more than one element or lens is used in a system, the object may also be virtual. The wily student will consult texts for a more complete understanding of these things. Only those who are not confused may proceed.
The lateral magnification, m, of an optical system is defined as the ratio of the transverse dimension y' of the final image to the transverse dimension y of the original object. For a single thin lens it may be shown that, subject to the sign conventions stated above, m =y^y = -io.
When both 
and i are positive, the negative sign
of the magnification denotes an inverted image.
The angular magnification, M, or magnifying power is defined as the ratio of the angular size seen through the optical system to the angular size seen directly. The experimental magnifying power is measured using a grid for an object. The number of boxes on the object which appears to correspond to one box on the image is the experimental magnifications. Through the looking glass, it looks like this
One word more. Microscopes and telescopes, at least simple ones are understood quite simply as follows. There are two lenses. The closest to the object is called the ``objective'' and the one closest to the viewer's eye is called the ``eye piece'' or ``ocular''. The eye piece is positioned close to the image formed by the objective, just closer than its focal length, so that the image formed by the eye piece is virtual and magnified, in other words, the eye piece functions as a simple magnifier, and that's it! There are of course some peculiarities, but onward: