Lenses

They are the basis of all optical instruments, including the eye.

A lens is simply a piece of transparent material such as glass, plastic or liquid with one or more curved faces, and the effect that it has on a beam of light depends on the extent and nature of this curvature. The five important types of tens are shown in Figure 1.

The curvatures of the surfaces are measured from within the solid so using the real is positive sign convention:

convex lens surfaces have a real and therefore positive radius of curvature;
concave lens surfaces have a virtual and therefore negative radius of curvature;
a convex lens has a real and therefore positive focal length;
a concave lens has a virtual and therefore negative focal length.

All distances are measured from the pole of the lens and for a thin lens this is almost coincident with the centre of the lens.

The strength of a lens is described in terms of either its focal length or its power. The power of a lens is defined as:

For example, a convex lens with a focal length of 10 cm will have a power of + 10, while a concave lens with a focal length of 5 cm will have a power of -20. There is no 'normal' power for a pair of glasses but my reading glasses have a power of +1.5.

Convex lenses have positive powers while concave lenses have negative powers. The power of a meniscus lens depends on which face of the lens is the more sharply curved.

Uses of lenses

The uses of lenses are covered in most books covering less advanced work. However a brief survey is given here as a practical guide.

Convex lenses:

Eye (variable focal length)
Glasses to correct for long sight
Microscope
Telescope objective
Camera (single lens system)
Projector

Concave lenses:

Wide-angle spyhole in doors
Glasses to correct for short sight
Wide-angle lens in coach rear windows
Eye lens in Galilean telescope

The eye pieces in telescopes and the objective lenses in cameras are often made of multiple lenses of both convex, concave and meniscus types.