The nickel\'s image in the figure below has twice the diameter of the nickel whe

Question

The nickel's image in the figure below has twice the diameter of the nickel when the lens is 2.78 cm from the nickel. Determine the focal length of the lens, Two converging lenses having focal lengths of f_1 = 11.5 cm and f_2 = 20.0 cm are placed d = 50.0 cm apart, as shown in the figure below. The final image is to be located between the lenses, at the position x = 30.5 cm indicated. How far to the left of the first lens should the object be positioned? What is the overall magnification of the system? Is the final image upright or inverted? upright inverted

Explanation / Answer

m = +2 = - di / do

di = - 2do

using lens equation,

1/f = 1/di + 1/do = 1/(-2do) + 1/do

1/f = 1/2do

f = 2do = 2 x 2.78 = 5.56 cm

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for f2:

di' = 50-30.5 = - 19.5 cm

f2 = 20 cm

1/f2 = 1/di' + 1/do'

1/20 = 1/(-19.5) + 1/do'

do' = 9.87 cm

for lens 1:

di = 50 - 9.87 = 40.13 cm

f1 = 11.5 cm

1/11.5 = 1/do + 1/40.13

do = 16.12 cm

b) m = (di / do) (di'/do') = (40.13/16.12) (-19.5 / 9.87)

m = 4.92

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