Work out combined lens power instantly with clear inputs, formula shown and shareable results.
Two thin lenses separated by a distance d combine as P = P1 + P2 - d.P1.P2. In contact the powers simply add, but separation always reduces the total for two positive lenses: +5 D and +3 D at 50 mm give 7.25 D rather than 8 D. This is the basis of every compound lens design.
Gullstrand equation
P = P1 + P2 - d P1 P2
In contact
P = P1 + P2 when d = 0
Because the second lens intercepts light that the first has already begun to converge, so it acts on a narrower beam and contributes less.
Yes, when d = 1/P1 + 1/P2. That afocal arrangement is exactly how a telescope's objective and eyepiece are set.