Shown in the figure here is a convergent lens placed inside a cell filled with a liquid. The lens has focal length `+ 20 cm` when in air and its material has refractive index 1.50. If the liquid has refractive index 1.60, the focal length of the system is

Options

A. `+`80 cm
B. `-` 80 cm
C. `-` 24 cm
D. `-` 100 cm

Answer

D

Explanation

`(1)/(f) = (n- 1) ((1)/(R_(1)) - (1)/(R_(2)) ) `
`(1)/(f_(1)) = (1.6 -1 ) ((1)/(infty ) - (1)/(20) ) = (-3)/(100)`
`(1)/(f_(2)) = (1.5 -1) ((1)/(20) - (1)/(-20) ) = (1)/(20)`
`(1)/(f_(3)) = (1.6 -1) ((1)/(-20) - (1)/(infty) ) = (-3)/(100)`
`(1)/(f_(eq)) = (-3)/(100) + (1)/(20) - (3)/(100) = (-1)/(100)`
`f_(eq) = -100` cm.