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.

Answer

`(f(1-2 costheta))/(1-cos theta),0`

Explanation

`(1)/(v)-(1)/(u)=(1)/(f)`
`(1)/(v)-(1)/(-f cos theta)=(1)/(f)`
`v=(f cos theta)/(cos-1)=-(f cos theta)/((1-cos theta))`
`m=(v)/(u)=(f cos theta//[cos theta-1])/(-f cos theta) rArr m=((1)/(1-cos theta))`
`therefore(A'B')/(AB)=((f cos theta)/(1-cos theta))//f cos theta`
`rArr A'B'=(f sin theta)/(1-cos theta)`
From similar triangles, `B'` lies on the principal axis of first lens.
`therefore y=o` and `x=2f-O'B'=2f-(f)/((1-cos theta))=(f(1-2cos theta))/((1-cos theta))`