A thin converging lens forms a real image of an object located far away from the lens. The image is formed at A at a distance 4x from the lens and height of the image is h. A thin diverging lens of focal length x is placed at `B [PB = 2x]` and a converging lens of focal length 2x is placed at `C [PC = 3x]`. The principal axes of all lenses coincide. Find the height of the final image formed.

Options

A. `h`
B. `(h)/(2)`
C. `4h`
D. `2h`

Explanation

From `2^(nd)` lens `(1)/(9v)-(1)/(2l)=(1)/(-l)` or `v=-2l`
`m_(1)=-1`
From `3^(rd)` lens `(1)/(v)-(1)/(-3l)=(1)/(2l)` or `v=6l`
`m_(2)=-2`
`h_(i)(m_(1)xxm_(2))h_(0)`
`=2h`