Two converging lenses of the same focal length f are separated by a distance 2f. The axis of the second lens is inclined at angle `theta=60^@` with respect to the axis of the first lens. A parallel paraxial beam of light is incident from left side of the lens. Find the coordinates of the final image with respect to the origin of the first lens.

Explanation

Using lens formula for `L_2,`

`1/v-1/(-f//2)=1/f`
or `v=-f`
This f length will be along PP' from point O'
(towards P).
`:. O'I_2'=f`
On x-axis this distance will be f `sec 60^@=2f.`
Since, `OO'=2f,` image will be formed at
origin.
Therefore `I_1 and I_2` both should be on this line,
which is also the x-axis. That's why for final
image we have taken projection of `OI_2'` on x-axis.