Two identical thin planoconvex glass lenses (refractive index `1.5)` each having radius of curvature of `20cm` are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index `1.7`. The focal length of the combination is

Options

A. `-25 cm`
B. `-50 cm`
C. `50 cm`
D. `-20 cm`

Answer

C

Explanation

`1/(f_(1))=(3/2-1)(1/(oo)-1/20)=1/40=1/(f_(3))`
`1/(f_(2))=(1.7-1)(1/(-20)-1/20)=(0.7)(-1/10)=-7/100`
`1/F=1/(f_(1))+1/(f_(2))+1/(f_(3))=1/40-7/100+1/40`
`=(5-40+5)/200=-1/50`
`F=-50 cm`