Two converging lenses having focal lengths of f 1 = 12.0 cm and f 2 = 20.0 cm ar

Question

Two converging lenses having focal lengths of f1 = 12.0 cm and f2 = 20.0 cm are placed d = 50.0 cm apart, as shown in the figure below. The final image is to be located between the lenses, at the position x = 30.9 cm indicated.

(a) How far to the left of the first lens should the object be positioned? __________ cm

(b) What is the overall magnification of the system? __________

(c) Is the final image upright or inverted?

Two converging lenses having focal lengths of f1 = 12.0 cm and f2 = 20.0 cm are placed d = 50.0 cm apart, as shown in the figure below. The final image is to be located between the lenses, at the position x = 30.9 cm indicated. How far to the left of the first lens should the object be positioned? __________ cm What is the overall magnification of the system? __________ Is the final image upright or inverted?

Explanation / Answer

you don't show the figure, so I will assume f1 is to the left and f2 to the right

we work backwards:

if the final image is 38 cm to the right of f1, it is 16 cm to the left of f2; we use the thin lens equation to find the object distance for the final image:

1/o + 1/i = 1/f

i=-16cm since the image is to the left of the lens, so

1/o = 1/19+1/16 => o = 8.7 cm to the left of f2 or 54-8.7 to the right of f1

the object for f2 is the image for f1, so we now find o for f1:

1/o + 1/i = 1/f
1/o + 1/45.3 = 1/8

o = 10 cm to the left of f1

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