Two identical thin planoconvex glass lenses (refractive index `1.5)` each having radius of curvature of `20cm` are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index `1.7`. The focal length of the combination is

Options

A. `- 25 cm`
B. `- 50 cm`
C. (c ) `50 cm`
D. `- 20 cm`

Answer

B

Explanation

From lens maker's formula `(1)/(f) = (mu - 1)((1)/(R_(1)) - (1)/(R_(2)))`

If `f_(1), f_(2)` are focal length of two plano convex lenses, then
`:. (1)/(f_(1)) = (1.5 - 1)((1)/(20) - (1)/(oo))`
`(1)/(f_(1)) = (0.5)((1)/(20)) = (1)/(40)` [As `R_(2)` is `oo`]
and `(1)/(f_(1)) = (1.5 - 1)((1)/(20) - (1)/(oo)) = (1)/(40)`
For concave lens of oil,
`(1)/(f_(3)) = (1.7 - 1)((-1)/(20) + (-1)/(20)) = 0.7 xx (-2)/(20) = (-7)/(100)`
focal length of the combination is given by,
`(1)/(f) = (1)/(f_(1)) + (1)/(f_(2)) + (1)/(f_(3))`
`(1)/(f) = (1)/(40) + (1)/(40) + ((-7)/(100))`
`= (5 + 5 - 14)/(200) = (-4)/(200) = (-1)/(50)`
`f = - 50 cm`