Two converging lenses having focal lengths of f1 10 cm and

Two converging lenses having focal lengths of f₁ = 10 cm and f₂ = 21 cm are placed 50 cm apart as shown in Figure. The final inverted image is to be located between the lenses at the position 37 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.

Solution

1/d_o + 1/di = 1/f

d_i = -(50 - 37) = -13 cm [ as the image is to the left of the lens ]

1/d_o = 1/21 + 1/13

do = 8.03 cm

The object for f₂ is the image for f₁ or (50 - 8.03 = 41.97) to the right of f1

1/do + 1/di = 1/f

1/do + 1/41.97 = 1/10

d_o = 13.13 cm [ to the left of f₁ ]