Basic Optical Principles
Focal Length & Power

There is a definite relationship between the power of a lens in diopters and the resulting focal length in meters. The stronger the power, the shorter the focal length, the weaker the power, the longer the focal length. This relationship may be expressed in the following formula: D = 1/f or f = 1/D

where D = power of the lens in diopters and f = focal length in meters.

Examples:

Caulculate Focal Lengths	Calculate Powers
D= +2.00 f=1/D f=1/+2.00 f=+0.5 m or +50 cm or +500 mm D=�7.50 f=1/D f=1/�7.50 f=�0.133m or�13.3 cm or �133 mm D=�10.00 f=1/D f=1/�10.00 f=�0.10 m or 10 cm or 100 mm	f=+7.7 cm D=1/f D=1/+.077m D=+13.00 D f= +0.222 m D=1/f D=1/+0.222 m D= +4.50 f= �571 mm D=1/f D=1/�.571 D= �1.75

The focal lengths of minus lenses are negative while those of plus lenses are positive. This can be explained by superimposing a plus and minus lens on the cartesian coordinate system explained earlier, and by following the convention of diagramming rays of light as traveling from left to right. As illustrated below, the focal points of minus lenses fall in the minus quadrant of the x axis while those of plus lenses fall in the plus quadrant.