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

B

Explanation

The intervening medium between the lenses will behave as a concave lens.
The refractive index of plano - convex lens, `mu_(1)=1.5`
and for concave lens, `mu_(2)=1.7`
`(1)/(F)=(1)/(f_(1))+(1)/(f_(2))+(1)/(f_(3))`
`=(mu_(1)-1)[(1)/(R)]+(mu_(2)-1)[(1)/((-R))-(1)/(R)]+(mu_(1)-1)[(1)/(R)-(1)/((-oo))]`
`=(2)/(R)[(mu_(1)-1)-(mu_(2)-1)]`
`=(2)/(R)[mu_(1)-1-mu_(2)+1]`
`(1)/(F)=(2(mu_(1)-mu_(2)))/(R)`
`F=(R)/(2(mu_(1)-mu_(2)))=(+20)/(2(1.5-1.7))`
`=-(10)/(0.2)=-50cm`