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

Options

A. `-15,10`
B. `-10, 15`
C. `75, 50`
D. `-75, 50`

Answer

A

Explanation

`(|P_(1)|)/(|P_(2)|)=(2)/(3)rArr (f_(2))/(f_(1))=(2)/(3)" …(i)"`
Focal length of their combination
`(1)/(f)=(1)/(f_(1))-(1)/(f_(2)) rArr (1)/(30)=(1)/(f_(1))-(1xx3)/(2f_(1))`
from (i)
`rArr" "(1)/(30)=(1)/(f_(1))[1-(3)/(2)]=(1)/(f_(1))xx(-(1)/(2))`
`therefore f_(1)=-15cm" "therefore f_(2)=(2)/(3)xxf_(1)=(2)/(3)xx15=10cm`