A split lens has its two parts separated by `a` and its focal length is `f`. An object is placed at a distance `(3f)/(2)` on the axis of undivided lens as shown. The distance between the virtual source is

Options

A. `(a)/(2)`
B. `2a`
C. `3a`
D. `(3a)/(2)`

Answer

C

Explanation

consider each part as separate lens with
`u=-(3f)/(2),f=f`
`(1)/(v)-(1)/(u)=(1)/(f)implies(1)/(v)-(1)/((-3f)/(2))=(1)/(f)`
`(1)/(v)=(1)/(f)-(1)/(3f)=(3-2)/(3f)`
`v=3f`
So each part will form a real image of the point object `O` at distance `3f` as shown.
Similar triangles, `OL_1L_2` and `OI_1I_2`
`(L_1L_2)/((3f)/(2))=(I_1I_2)/((3f)/(2)-3f)implies(a)/((3f)/(2))=(I_1I_2)/((9f)/(2))`
`I_1I_2=3a`