Question

3. Consider the compound optical system shown in the diagram, where two thin lenses of focal lengths 7.5 cm (left lens) and 8.5 cm (right lens) are separated by a distance 32 cm.

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a) If an object is placed a distance d_o = 15.3 cm to the left of the first lens (the left one) as shown in the figure, how far to the right of that lens, in centimeters, 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 lens)?

d) What is the image distance, in centimeters, for the second lens?

e) What is the magnification of the second lens?

Answer 1

a)

using lens formula

1/f = 1/v - 1/u

1/7.5 = 1/ v + 1/15.3

v = 14.71 cm

b)

m1 = - v/u = - 14.71/15.3 = 0.9615

c)

object distance for 2nd lens

u' = 32 - 14.71 = 17.29 cm

d)

using lens formula for right lens

1/8.5 = 1/ v' + 1/17.29

v' = 16.72 cm

e) m2 = - 16. 72/17.29 = - 0.967

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