Question

Two converging lenses having focal lengths of f₁ = 8 cm and f₂ = 18 cm are placed 49 cm apart as shown in Figure. The final inverted image is to be located between the lenses at the position 39 cm to the right of the first lens. How far to the left of the first lens should the object be positioned?Express the answer (in cm) with one decimal place.

Answer 1

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