Consider the compount optical system shown in the diagram, where two thin lenses

Question

Consider the compount optical system shown in the diagram, where two thin lenses of coal lengths 9.5 cm (left lens) and 2.5 cm (right lense) are separated by a distance 47 cm.

a) If object is placed d0=14.2 cm to the left of the left lense, how far to the right of that lens is the image formed?

b) What is the magnification of the first lens?

c) What is the object distance, in centimeters, for the second lens (the right lense)?

d) What is the imge distance, in centimeteres, for the second lens?

e) What is the magnification of the second lens?

Explanation / Answer

1/f = 1/u + 1/v

1/9.5 = 1/14.2 + 1/v

v = 28.70 cm

distancebetween 2 lenses = 47 cm

object distance for lens 2 = 47-28.70 = 18.3 cm

for lens 2

1/f2 = 1/u2 + 1/v2

1/2.5 = 1/18.3 + 1/v2

v2 = 2.8955 cm

the image is formed 2.8955 cm right of lens 2

so from lens 1 image distance = 47+2.895 = 49.8955 cm

a) from first lens image distance = 28.70 cm

b) M1 = -v1/u1 = -28.7/14.2 = -2.021

c) for second lens object distance =47-28.7 = 18.3 cm

d) for second lens image distance = 2.8955 cm

e) M2 = -v2/u2 = -2.8955/18.3 = -0.1582

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