A plano-convex lens `(mu = 1.5)` of aperture diameter `8 cm` has a maximum thickness of `4mm`. The focal length of the lens relative to air is

Options

A. `+ 20 cm`
B. `+ 40 cm`
C. `+ 60 cm`
D. `+80 cm`

Answer

B

Explanation

`R^(2) = (R - t)^(2) + r^(2)`
`R^(2) = R^(2) + t^(2) - 2Rt + r^(2)`
`r^(2) = 2Rt (t^(2) "is neglected")`
`R = (r^(2))/(2t) = (4 xx 4)/(2 xx 0.4) = 20 cm`
`R = 20 cm`
`:, (1)/(f) = (1.5 - 1) ((1)/(oo) -(1)/(-20))`
`(1)/(f) = (.05)/(20) :. f = + 40 cm`