A bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. Refractive index n of the first lens is 1.5 and that of the second lens is 1.2. Both the curved surface are of the same radius of curvature R=14 cm. For this bi-convex lens, for an object distance of 40 cm, the image distance will be `

Options

A. `-280.0cm`
B. 40.0 cm
C. 21.5 cm
D. 13.3 cm

Answer

B

Explanation

The focal length `(f1_(1))` of the lens with `n=1.5 is given by
`(1)/(f)=(n_(1)-1)[(1)/(R_(1))-(1)/(R_(2))]`
`=(1.5-1)[(1)/(14)-(1)/(infty)]` `=(1)/(28)`
The focal length (f_(2)) of the lens with `n=1.2` is given by
`(1)/(f_(2))=(n_(2)-1)[(1)/(R_(1))-(1)/(R_(2))]`
`=(1.2-1)[(1)/(infty)-(1)/(-14)]` `=(1)/(70)`
The focal length F of the combination is
`(1)/(F)=(1)/(f_(1))+(1)/(f_(2))=(1)/(20)`
Applying lens formula for the combination of lens
`(1)/(V)-(1)/(U)=(1)/(f)` `implies` `(1)/(V)-(1)/(-40)=(1)/(20)` `implies` `V=40cm`