Question

# Two converging lenses having focal lengths of f1 = 11 cm and f2 = 19 cm...

Two converging lenses having focal lengths of f1 = 11 cm and f2 = 19 cm are placed 50 cm apart as shown in Figure. The final inverted image is to be located between the lenses at the position 38 cm to the right of the first lens. How far (in cm) to the left of the first lens should the object be positioned? Express the answer (numerical value only) with one decimal place.

given

focal lengths of

f1 = 11 cm

f2 = 19 cm

final inverted image is to be located between the lenses at the position 38 cm to the right of the first lens.

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 12 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=-12cm since the image is to the left of the lens, so

1/o = 1/19+1/12=> o = 7.40 cm to the left of f2 or 50-7.40to 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 + 1/42.6 = 1/11

o = 14.920 cm to the left of f1

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