The mathematics is easy. A lens power in dioptres is 1 divided by its focal length in metres. So a 300mm lens is 1/0.3 = 3.3 dioptres.

If you have two lenses and want to work out their combined focal length when placed together, just convert to dioptres, add them together then convert back again:

e.g. a 300mm lens and a 400mm lens together. We already know that 300mm = 3.3D. 400mm = 1/0.4 = 2.5D so the combined power is 5.8D.

To convert back to focal length, 1/5.8 = 0.172 metres or 172mm.

Another rule of thumb is that a 1 dioptre lens will focus parallel beams of light at a point 1 metre away. Double the power to 2 dioptres and the focus point halves to 0.5 metre, etc.

Steve.