Two systems are formed from a converging lens and a diverging lens, as shown in

Question

Two systems are formed from a converging lens and a diverging lens, as shown in parts a and b of the drawing. (The point labeled "F_converging" is the focal point of the converging lens.) An object is placed inside the focal point of lens 1 at a distance of 6.50 cm to the left of lens 1. The focal lengths of the converging and diverging lenses are 15.0 and -20.0 cm respectively. The distance between the lenses is 50.0 cm. Determine the final image distance for each system, measured with respect to lens 2.

Explanation / Answer

from the lens equation

1/di1 = 1/f1 - 1/ do1 = 1/15 - 1/6.5

di1= -11.47 cm

di2 = 11.47 cm +50 cm = 61.47 cm

1/di2 = 1/f2 - 1/ do2 = 1/-20 - 1/61.47

di2 = -15.09 cm

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(b)

1/di1 = 1/f1 - 1/ do1 = 1/-20 - 1/6.5

di1 = -4.90cm

do2 = 4.9 + 50 = 54.9 cm

1/di2 = 1/f2 - 1/ do2

= 1/15 - 1/54.9

di2 = 20.63 cm

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