1.

A convex lens is in contact with a concave lens. The magnitude of the ratio of their focal lengths is (2)/(3). Their equivalent focal length is 30 cm. What are their individual focal lengths?

Answer»

`-75CM, 50cm`
`-10M, 15cm`
`75cm, 50cm`
`-15cm, 10 cm`

Solution :Let focal length of convex and concave lenses be `+f_(1) and -f_(2)cm` respectively. Then as per question `((f_(1))/(f_(2)))=(2)/(3) or |f_(2)|=(3)/(2)|f_(1)|` and focal length f of combination is 30 cm.
As `(1)/(f)=(1)/(f)+(1)/(f_(2))`, hence `(1)/(30)=(1)/(f_(1))+(1)/((-(3)/(2)f_(1)))=(1)/(f_(1))-(2)/(3f_(1))=(1)/(3f_(1))RARR f_(1)=10 cm and f_(2)=-15cm`.


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