A convergent doublet of separated lens correct for spherical aberration, are separated by `2m` and has an equivalent focal lenth of `10cm`. Calculate the focal length of its component lenses.

Options

A. `f_(1)=18cm, f_(2)=10cm`
B. `f_(1)=20cm, f_(2)=28cm`
C. `f_(1)=20cm,f_(2)=18cm`
D. `f_(1)=24cm,f_(2)=18cm`

Explanation

(c) Since the doublet is corrected for spherical aberration, it satisfies the following condition
`f_(1)-f_(2)=d=2cm`
`f_(1)=f_(2)+2cm`
Let theh equivalent focal length `=F`
`F=(f_(1)f_(2))/(f_(1)+f_(2)-d)=10cm`
Solving, it `f_(1)=20cm, f_(2)=18cm`