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Question: What is the focal length of a convex lens of focal length 30 cm in contact with a concave lens of focal length 20 cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.

Answer:

Focal length of the convex lens, f1 = 30 cm

Focal length of the concave lens, f2 = −20 cm

Focal length of the system of lenses = f

The equivalent focal length of a system of two lenses in contact is given as:

1 / f = 1 / f₁ + 1 / f₂

1 / f = 1 / 30 - 1 / 20 = 2 - 3 / 60 = - 1 / 60

So f = - 60 cm

Hence, the focal length of the combination of lenses is 60 cm. The negative sign indicates that the system of lenses acts as a diverging lens.

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Question: What is the focal length of a convex lens of focal length 30 cm in contact with a concave lens of focal length 20 cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.

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