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. 20 cm
B. 40 cm
C. 60 cm
D. 80 cm

Answer

B

Explanation

Focal length of left lens.
`(1)/(f_1)=(1.5-1)((1)/(14)-(1)/(infty))=(0.5)/(14)`
Focal length of right lens, `(1)/(f_2)=(1.2-1)((1)/(infty)-(1)/(-14))=(0.2)/(14)`
Equivalent focal length
`(1)/(F)=(1)/(f_1)+(1)/(f_2)=(0.5)/(14)+(0.2)/(14)=(0.7)/(14)=(1)/(20)`
For bi-convex lens.
`(1)/(v)-(1)/(-40)=(1)/(F)=(1)/(20)`
`(1)/(v)=(1)/(20)-(1)/(40)=(1)/(40)`
`v=40cm`