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

For `1^(st) ` part (lens)
`(1)/(f_(1)) = (n_(1) - 1) ((1)/(R_(1)) - (1)/(R_(2)))`
`rArr (1)/(f_(1)) = [ 1.5 -1] ((1)/(14) - (1)/(oo))`
`f_(1) = 28`

For ` 2^(nd) ` part (lens)
`(1)/(f_(2)) = (1.2 -1) ((1)/(oo) -(1)/(-14))`
`rArr f_(2) = 70 cm`
`(1)/( f_(eq)) = (1)/(f_(1)) + (1)/(f_(2)) = (1)/(28)) + (1)/(70)`
`= (1)/(20) rArr f_(eq) = 20 cm `
`(1)/(v) - (1)/(u) = (1)/(f_(eq))`
`rArr (1)/(v) = (1)/(20) - (1)/(40) rArr (1)/(v) = (1)/(40) rArr v = 40 cm ` (as u = - 40 cm )