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

Answer 1

For the diverging lens
f2 = -28 cm
v =-22.1
u = vf/ (v-f) = (22.1*28) / (-22.1+28) = 104.88 cm to the left of the diverging lens
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The distance between the two lenses is 56cm
Therefore v fot the converging lens is to the left of that by a distance
= 56-104.88 = -48.88 cm

for the converging lens
v = -48.88 cm
f = 24 cm
u = vf/ (v-f) = -48.88 * 24/ (-48.88 - 24) = 16.1 cm

The object is at a distance of 16.1 cm to the left of the converging lens.