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.

(a) (b) (c) (d) (e) p1 Lens 1 d Lens 2 i2 M R/V I/NI Side +4.0 C, 9.0 14 D, -9.0

Explanation / Answer

Part A)

Start with the first lens

1/f = 1/p + 1/i

1/9 = 1/4 + 1/i

i = -7.2

Then that is the object for the second lens and it is 7.2 + 14 cm away

That is 21.2 cm

For the second lens

1/f = 1/p + 1/i2

1/-9 = 1/21.2+ 1/i2

i2 = -6.32 cm

Part B)

M = -i/p1 times -i2/p2

M = -(-7.2)/(4) times -(-6.32)/(21.2)

M = .537

Part C)

Since i2 is negative, the final image is virtual

Part D)

Since M is positive, the final image is noninverted

Part E)

Since i2 is negative, it is on the same side of lens 2 as the object

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