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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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Solution
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/"f"_1 + 1/"f"_2`
`1/"f" = 1/30 - 1/20`
`1/"f" = (2 - 3)/60`
`1/"f" = -1/60`
∴ 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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