Two-lens systems. In the figure, stick figure O (the object) stands on the commo

Question

Two-lens systems. In the figure, stick figure O (the object) stands on the common central axis of two thin, symmetric lenses, which are mounted in the boxed regions. Lens 1 is mounted within the boxed region closer to O, which is at object distance p1. Lens 2 is mounted within the farther boxed region, at distance d. Each problem in the table refers to a different combination of lenses and different values for distances, which are given in centimeters. The type of lens is indicated by C for converging and D for diverging; the number after C or D is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated). Find (a) the image distance i2 for the image produced by lens 2 (the final image produced by the system) and (b) the overall lateral magnification M for the system, including signs. Also, determine whether the final image is (c) real or virtual, (d) inverted from object O or noninverted, and (e) on the same side of lens 2 as object O or on the opposite side.

Explanation / Answer

a)

for lens 1 :

f1 = focal length = 9.2 cm

do1 = object distance = 18 cm

di1 = image distance by lens 1

using the lens equation

1/f1 = 1/do1 + 1/di1

1/9.2 = 1/18 + 1/di1

di1 = 18.82 cm

for lens 2 :

f2 = focal length = - 8.6 cm

do2 = object distance = d - di1 = 35 - 18.82 = 16.18 cm

di2 = image distance by lens 2

using the lens equation

1/f2 = 1/do2 + 1/di2

1/(-8.6) = 1/16.18 + 1/di2

di2 = - 5.62 cm

b)

m1 = magnification by lens 1 = - di1/do1 = - 18.82 / 18 = - 1.05

m2 = magnification by lens 2 = - di2 /do2 = - ( - 5.62) / 16.18 = 0.35

Total magnification = m1 m2 = (- 1.05) (0.35) = - 0.3675

c)

final image is virtual as it is produced by diverging lens which always produce virtual image

d)

the image is inverted from the object

e)

it is on the same side

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