Two this lenses, when in contact, produce a combination of power `+10` diopters. When they are 0.25 m apart, the power reduces to `+6` diopters. The focal length of the lenses are…. `m` and …`m`.

Answer

A, B

Explanation

`P_1+P_2=10 m^-1`
`P_1+P_2-(0.25)P_1P_2=6 m^-1`
From these two expressions, we get `P_1P_2=16 cm^-2`
`P_1-P_2=sqrt((P_1+P_2)^2-4P_1P_2`
`=sqrt((10^-1)^2-4(16^-1))=16m^-1`
:' `P_1=8m^-1 and P_2=2m^_1`, Hence
`f_1=(1)/(P_1)=(1)/(8)m=0.125 m and `f_2=(2)/(P_2)=(1)/(2)m=0.5m`