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 19.4 cm to the left of the diverging lens. How far is the object from the converging lens?

Answer 1

here,

for the diverging lens

the focal length , f2 = - 28 cm

the image distance , di2 = - 19.4 cm

let the object distance be do2

using the lens formula

1/f2 = 1/di2 - 1/do2

1/(-28) = 1/(- 19.4) - 1/do2

solving for do2

do2 = - 63.2 cm

for the converging lens

the focal length , f1 = 24 cm

the image distance , di1 = do2 + 56 cm

di1 = - 7.2 cm

let the object distance be do1

using the lens formula

1/f1 = 1/di1 - 1/do1

1/24 = 1 /(-7.2) - 1/do1

do1 = - 5.54 cm

the object is placed 5.54 cm to the left of converging lens