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

Q 9.10: What is the focal length of a convex lens of focal length 30cm in contact with a concave lens of focal length 20cm? Is the system a converging or a diverging lens? Ignore the thickness of the lenses.

Answers (1)

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When two lenses are in contact, the equivalent is given by 

\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}

where f_1 and f_2 are the focal length of two individual lenses.

So, given,

f_1 = 30 cm, and f_2 = -20cm (as focal length of the convex lens is positive and that of the concave lens is negative by convention),

putting these values together, 

 \frac{1}{f}=\frac{1}{30}+\frac{1}{-20}

\frac{1}{f}=-\frac{1}{60}

f = -60cm

Hence, the equivalent focal length will be -60 cm and since it is negative, it is behaving as a concave lens, which is also called diverging lens.

Posted by

Pankaj Sanodiya

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