A thin convex lens of focal length 'f' is put on a plane mirror as shown in the figure . When an object is kept at a distance 'a' from the lens - mirror combination , its image is formed at a distance `(a)/(3)` in front of the combination . The value of 'a' is :-

Options

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

Answer

B

Explanation

The formula for combination of lens and mirror if there is no gap in between the mirror and convex lens is given by
`(1)/(f.)-2((1)/(f_("lens")))+(1)/(f_("mirror"))`
`=-2((1)/(f))+(1)/(oo)=(-2)/(f)`
For concave mirror,
`(1)/(f.)=(1)/(u)+(1)/(v)=(-3)/(a)+(-1)/(a)=(-4)/(a)`
`rArr" "(-2)/(f)=(-4)/(a)`