Question

The power of a lens is expressed in diopters (D). You have probably seen this used in eyeglass prescriptions where converging lenses (reading glasses) are prescribed in positive diopters and diverging lenses (correction for near-sightedness) are prescribed using negative diopters. The power, in diopters, is obtained by taking the inverse of the focal length, after the focal length is converted to meters. The power of two or more adjacent lenses is simply the sum of their individual powers. D = D1 + D2 + ...+ Dn Find the combined power of three close-up lenses for acamera that rae rated + 1D, + 2d, and + 3D. What is the focal length of each lens? What is the focal length of the stack of three lenses?

Answer 1

combined power P = P1 + P2 + P3 = 1D + 2D + 3D = 6D <----answer

P1 = 1/f1

f1 = 1/P1 = 1/1 = 1m = 100cm <---answer

for second lens

P2 = 1/f2

f2 = 1/p2 = 1/2 = 0.5m = 50 cm <--answer

for third lens

P3 = 1/f3

f3 = 1/p3 = 1/3 = 0.333 m = 33.3 cm <-answer

combined focal length 1/F = 1/f1 + 1/f2 + 1/f3

1/F = P1 + P2 + P3 = P

1/F = P

F = 1/P = 1/6 m

focal length of the stack = F = 100 /6 cm = 16.7 cm <------answer