Physics??,...glass lens??

Question

Two converging lenses are placed 20.0 cm apart. If the first lens has a focal lenght of 10.0 and the second has the focal lenght of 20.0 . Locate the final image formed of an object 30.0 cm in front of the 1at lens. Find the mganification.

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Answer 1

See the refs. 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 = 0.3 m; f1 = 0.1 m; sep = 0.2 m; f2 = 0.2 m; v2 = unknown

Solving,

v1 = 1/(1/f1-1/u1) = 0.15 m

u2 = sep-v1 = 0.05 m

v2 = 1/(1/f2-1/u2) = -0.0666667 m

Final Image location relative to lens 2 = v2 = -0.0666667 m (left of lens 2)

Final Image location relative to lens 1 = v2+sep = 0.1333333 m (right of lens 1)

Final Image location relative to object = v2+sep+u1 = 0.4333333 m

Magnification = v1v2/(u1u2) = -0.6666667

Answer 2

the final image of the 1st lens is di=15cm

and 2nd lens is di=60cm

di means distance of the image

magnification= 0.5