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

Options

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

Answer

D

Explanation

Equivalent power = 1/0.3 = 10/3D
Let `P_1` be the magnitude of power of concave lens and `P_2` be the power of convex lens then . Power of and concave lens is negative and hence we can write the following equation :
`P_2 -P_1 =10/3 " "...(1)`
Overall power is positive and hence `P_2` must be greater than `P_2`.
`P_1/P_2 =2/3 " "...(2)`
Substituting `P_1` from equation (2) into equation (1) we get the following.
`P_2 =2/3 P_2 =10/3`
`implies P_2 = 10 D and P_1 =20/3D`
Focal length of concave lens = `-(100)/(20//3)cm = -15 cm`
Focal length of convex lens `= 100/10 cm = 10 cm `
Hence option (d) is correct .