A compound lens system consists of a converging lens with focal length 20.0cm, a

Question

A compound lens system consists of a converging lens with focal length 20.0cm, and a diverging lens with focal length -20.0cm, separated by 60.0cm. An object 4.0cm tall is placed 40.0cm in front of the converging lens (see figure). How tall is the final image produced by the compound lens system?

A compound lens system consists of a converging lens with focal length 20.0cm, and a diverging lens with focal length -20.0cm, separated by 60.0cm. An object 4.0cm tall is placed 40.0cm in front of the converging lens (see figure). How tall is the final image produced by the compound lens system?

Explanation / Answer

From the lens equation 1/v + 1/u =1/f, we get, the image distance for the convex lens is, 1/v = 1/20 -1/40 cm^-1 . So image distance = 40 cm from lens 1.

This image acts as an object for lens 2, with an object distance of 60-40cm = 20cm.
The focal length is f2=-20cm.
From lens equation, 1/v = -1/20-1/20. so, v=-10cm.

Now image size (final) = object size x (image distance / object distance)lens1 x (image distance / object distance)lens2 = 4 x 1 x .5 = 2 cm. (answer)

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