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 with in the boxed region closer to O, which is at object distance p_1. Lens 2 is mounted with in 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 the image distance i_2 for the image produced by lens 2 (the final image produced by the system) and the overall lateral magnification M for the system, including signs. Also, determine whether the final image is real or virtual, inverted from object O or noninverted, and on the same side of lens 2 as object O or on the opposite side.

Explanation / Answer

for lens 1

object distance p1 = 18 cm

focal length f1 = +20 cm

image distance i1 = ?

from lens equation

1/p1 + 1/i1 = 1/f1

1/18 + 1/i1 = 1/20

i1 = -180 cm

magnification m1 = -i1/p1 = 180/18 = 10

for second lens

p2 = d+i1 = 180+11 = 191 cm

f2 = -8.1

1/p2 + 1/i2 = 1/f2

1/191 + 1/i2 = 1/8.1

i2 = 8.46 cm

image distance i2 = 8.46 cm

magnification m2 = -i2/p2 = -8.46/191 = -0.044

M = m1*m2 = 10*0.04 = -0.44

a)

8.46 cm

b)

M = 0.44

c)
real

d)

inverterd

e)

other side of lens

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