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. For this problem, p1 = 9.9 cm, lens 1 is diverging, d = 16 cm, and lens 2 is converging. The distance between the lens and either focal point is 6.1 cm for lens 1 and 6.3 cm for lens 2. (You need to provide the proper sign).

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 +9.9 D, 6.1 16 C, 6.3

Explanation / Answer

Part A)

Start with the first lens

1/f = 1/p + 1/i

1/-6.1 = 1/9.9 + 1/i

i = -3.77

Then that is the object for the second lens and it is 3.77 + 16 cm away

That is 19.77 cm

For the second lens

1/f = 1/p + 1/i2

1/6.3 = 1/19.77 + 1/i2

i2 = 9.25 cm

Part B)

M = -i/p1 times -i2/p2

M = -(-3.77)/(9.9) times -(9.25)/(19.77)

M = -.178

Part C)

Since i2 is positive, the final image is real

Part D)

Since M is ngative, the final image is inverted

Part E)

Since i2 is positive, it is on the opposite side of the lens at the object

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