# Focal length

Approximating the focal length of simple lenses.

Admit it, you have a load of old lenses that you have no idea what there focal length is! You want a quick easy way of finding out what the focal length of a given lens is.

Quick note on focal length.
The focal length, f, of a lens is the length at light coming from a large distant source is brought into a focus from the centre line of the lens. It can be measured in meters, centimetres or millimetres. However, it is often quoted in “dioptres”. This is the 1 divided by the focal length in meters. The positive values are for converging (magnifying) lenses and negative are for diverging or concave lenses - think that the surfaces “cave in”. These give a virtual (or imaginary) focus So a focal length of +10D (10 dioptres) has a focal length of 1/10 m or 10cm or 100mm. It is a magnifying type lens. Similarly a focal length of -4D has a focal length of ¼ m or 25cm or 250mm. It is a concave lens.
Concave lenses are used to correct short-sightedness (myopia) and convex lenses are used to correct long-sightedness (presbiopia).

To estimate the length of lenses:

Convex lens
In a dark room choose a distant bright light source a single window at the far end of the room is a good choice. Use the near wall to focus the image from the window (you may want to use a piece of white paper). The distance from the focussed image to the lens is a good approximation to the focal length.

Concave lens
This is not so intuitive but please don’t give up. Using a pair of compasses put the pivot and pencil ends either side of the lens under question across the diameter. Mark a circle using this radius. Move the lens so that the bright area it creates just covers this circle. You may need a directed light source such as a projector for this to replace the window source. If you do, the further it is away the better. Looking at the ray diagram it is easy to see that the focal length on the virtual side is the same distance as when the bright circle is twice the size of the lens. --D.B.Ferguson 21:02, 8 September 2006 (BST)