Question

Two identical diverging lenses are separated by 20 cm. The focal length of each lens is -9.8 cm. An object is located 4.7 cm to the left of the lens that is on the left. Determine the final image distance relative to the lens on the right.

Answer 1

The key to this kind of problem is that the 1st (left) lens's

(Intermediate) image is the 2nd (right) lens's object. Then using notation from

ref. 1 (+uN is object distance to left of lens N and +vN is image distance to

right of lens N), we have initially:

u1 = 47 cm; f1 =-9.8 cm; sep = 20 cm; f2 =-9.8 cm; v2 = TBD

Solving,

v1 = 1/(1/f1-1/u1) = -8.11 cm

u2 = sep-v1 = 11.89 cm

v2 = 1/(1/f2-1/u2) = -5.37 cm

Final Image location relative to lens 2 = |v2| = 5.37 cm