A thin equiconvex glass lens `(mu_(1) = 1.5)` of radius of curvature 'R' and a thin plano-concave lens `(mu_(2) = 1.4)` are kept in contact and the plane surface is silvered. This lens system is placed in air. When a point object is placed at a distance `20 cm` from the lens system on its principal axis, the image formed by the lens system coincides with the object. Then the value of radius of curvature 'R' is

Options

A. `12 cm`
B. `18 cm`
C. `24 cm`
D. `30 cm`

Answer

A

Explanation

`(1)/(f_(1)) = (1.5 - 1) ((1)/(R ) + (1)/(R )) = (1)/(R )`
`:. f_(1) = R`
`(1)/(f_(2)) = (1.4 - 1) ((1)/(-R ) - (1)/(oo))`
`(1)/(f_(2)) = (0.4)/(R )`
`-(1)/(F) = (2)/(f_(1)) + (2)/(f_(1)) + (2)/(f_(2)) - (1)/(f_(m))`
Since image conicides wit the object,
`F = -10 cm`
`(-1)/(-10) = (2)/(R ) + 2 ((-0.4)/(R )) - (1)/(oo)`
`(1)/(10) = (2)/(R ) - (0.8)/(R )`
`(1)/(10) = (1.2)/(R )`
`:. R = 12 cm`