A convex lens is in contact with concave lens. If the ratio of their powers is `2/3` and focal length of the combination is 30 cm, then individual focal lengths are

Options

A. 75 cm and -50 cm
B. `-75` cm and 10 cm
C. 15 cm and `-10` cm
D. `15` cm and 10 cm

Answer

A, C, D

Explanation

For concave lens `P_2` is negative
`P_1=1//f_1` `P_2=1//f_2`
Let `f_1` and `P_1` are the focal length and power of concave lens. `f_2` and `P_2` are the focal length and power of convex lens.
The focal length of combined lens f = 30 cm
Now, `(P_1)/(P_2)=(-2)/(3)`
`therefore(f_2)/(f_1)=(-2)/(3)`
`implies f_2=-f_1xx2/3` ............(1)
Now `1/f=(-1)/(f_1)+(1)/(f_2)`
`(1)/(30)=(-1)/(f_1)+(3)/(2f_1)` (From eqn.1)
`=(-1)/(2f_1)`[2+3]
`impliesf_1=(-30)/(2)(5)=-15` cm
Now,`f_2=-f_1xx2/3=(+15(2))/(3)=10` cm
Hence `f_1=-15` cm,`f_2=10` cm