Two converging lenses are placed D = 60.0 cm apart. The initial object is placed

Question

Two converging lenses are placed D = 60.0 cm apart. The initial object is placed o1 = 28.7 cm in front of the first lens. The focal length of the second lens is known to be f2 = 25.3 cm which produces an image on a screen 17.3 cm from the second lens.  (Figure 1)

Part A

What is the focal length of the first lens?

Part B

What is the total linear magnification for the system?

Part C

If the screen is moved to twice it's distance from the second lens and the lenses are left in place, where should the first object be moved to produce a clear image on the screen?

Part D

What is the total linear magnification for this second arrangement?

Explanation / Answer

a)

for the second lens :

f2 = 25.3 cm

do2 = object distance for second lens

di2 =  image distance for second lens = 17.3 cm

using the lens equation

1/f2 = 1/do2 + 1/di2

1/25.3 = 1/do2 + 1/17.3

do2 = - 54.7 cm

di1 = image distance for lens 1 = D + 54.7 = 60 + 54.7 = 114.7 cm

f1 = ?

do1 = object distance for lens 1 = 28.7 cm

using the equation

1/f1 = 1/do1 + 1/di1

1/f1 = 1/28.7 + 1/114.7

f1 = 22.96

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