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

Options

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

Answer

B

Explanation

`(1)/(f_(1))=(mu-1)[(1)/(R_(1))-(1)/(R_(2))]`
`(1)/(f_(1))=(1.5-1)[(1)/(14)-(1)/(infty)]`
`(1)/(f_(1))=(0.5)/(14)`
`(1)/(f_(2))=(1.2-1)[(1)/(infty)-(1)/(-14)]`
`(1)/(f_(2))=(0.2)/(14)`
`(1)/(f)=(1)/(f_(1))+(1)/(f_(2))=(0.5)/(14)+(0.2)/(14)`
`(1)/(f)=(0.7)/(14)`
`(1)/(v)=(7)/(140)-(1)/(40)=(1)/(20)-(1)/(40) `
`(1)/(v)=(2-1)/(40)`
`v=40 cm`