## The thin Lens Equation

If we assume a lens has no thickness, the following equation relating the focal length f, the object length u and the image length v can be derived:

The following points must be noted.

• If either of u, v are imaginary then the corresponding values of u, v are negative.

• The value of f is positive for a concave or converging lens and negative for a convex or diverging lens.

• u or v are negative if rays of light must be constructed back to the position of the object or image. It is possible for an image to have a negative value.

Example:. The diagram below illustrates the formation of an image by a concave or converging lens. The object is further from the lens than the focal length and real. The focal length f is also real because the lens is concave.

If f=20 cm and u=50 cm,