Question

A converging lens (f1 = 24.0 cm) is located 56.0 cm to the left of a diverging lens (f2 = -28.0 cm). An object is placed to the left of the converging lens, and the final image produced by the two-lens combination lies 20.0 cm to the left of the diverging lens. How far is the object from the converging lens?

Answer 1

here,

for the seccond lens

the image distance , di2 = - 20 cm

focal length , f2 = - 28 cm

let the object distance be do2

using the lens formula

1/f2 = 1/di2+ 1/do2

- 1/28 = 1/do2 - 1/20

solving for do2

do2 = 70 cm

for the first lens

the image distance , di1 = 56 - do2 = - 14 cm

the object distance be do1

focal length ,f = 24 cm

using the lens formula

1/f1 = 1/di1 + 1/do1

1/24 = - 1/14 + 1/do1

do1 = 8.84 cm

the object is placed 8.84 cm to the left of converging lens