Question

A converging lens with a focal length of 4.0 cm is to the left of a second identical lens. When a feather is placed 12 cm to the left of the first lens, the final image is the same size and orientation as the feather itself. What is the separation between the lenses?​

Answer 1

The distance of separation between the lenses is determined as 12 cm.

Distance of image formed by the first lens

The distance of the image formed by the first lens is calculated as follows;

1/d₁ = 1/f - 1/di₀

1/di₁ = 1/4 - 1/12

1/di₁ = 2/12

1/di₁ = 1/6

di₁ = 6 cm

Find the final position of the image

Use magnification formula as shown below;

M = (di₁di₂)/(d₀₁d₀₂)

1 = (di₁di₂)/(d₀₁d₀₂)

di₂ = (d₀₁d₀₂)/(di₁)

di₂ = (12 x d₀₂)/(6)

di₂ = 2d₀₂

1/f = 1/ d₀₂ + 1/di₂

1/f =  1/ d₀₂ + 1/2d₀₂

1/f = 1.5/d₀₂

d₀₂ = 1.5f

d₀₂ = 1.5(4 cm) = 6 cm

Distance between the two converging lens

D = di₁ + d₀₂

D = 6 cm + 6 cm

D = 12 cm

Thus, the distance of separation between the lenses is determined as 12 cm.

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