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. (c ) `21.5 cm`
D. `13.3 cm`

Answer

B

Explanation

using lens maker's formula
`(1)/(f) = (mu - 1)((1)/(R_(1)) - (1)/(R_(2)))`
For first plano convex lens,
`(1)/(f_(1)) = (1.5 - 1)((1)/(14) - (1)/(oo)) = (1)/(28)`
For second plano convex lens,
`(1)/(f_(2)) = (1.2 - 1)((1)/(oo) - (1)/(-14)) = (1)/(70)`
If `f` is combined focal length of bi-convex lens,
then `(1)/(f) = (1)/(f) + (1)/(f_(2)) = (1)/(28) + (1)/(70) = (5 + 2)/(140) = (1)/(20)`
`f = 20 cm`
For this lens, `u = - 40 cm, v = ?`
From `(1)/(v) - (1)/(u) = (1)/(f)`
`(1)/(v) = (1)/(f) + (1)/(u) = (1)/(20) - (1)/(40) = (1)/(40)`
`v = 40.0 cm`