Two lenses of focal lengths 0.20 m and 0.30 m are kept in contact with each other. Calculate the resultant focal length of the combination. Also calculate the powers of the individual lenses and that of the equivalent lens.

Explanation

For two lenses in contact, `(1)/(f)=(1)/(f_(1))+(1)/(f_(2))`. Given `f_(1)=0.20m, f_(2)=0.30m`.
`(1)/(f)=(1)/(0.20)+(1)/(0.30)`
`(1)/(f)=5+3.333=8.333`
`therefore f=0.12m`.
Power of the first lens `P_(1)=(1)/(f_(1))=(1)/(0.20)=5D`.
Power of the second lens `P_(2)=(1)/(f_(2))=(1)/(0.30)=3.333D`.
Power of the equivalent lens `P=(1)/(f)=(1)/(0.12)=8.333D`.
or `P=P_(1)+P_(2)=8.333D`.