A converging mirror is placed on the right hand side of a converging lens as shown in the figure. The focal length of the mirror and the lens are 20 cm and 15 cm, respectively. The separation between the lens and the mirror is 40 cm and their principal axis coincide. A point source is placed on the principal axis at a distance d to the left of the lens. If the final beam comes out parallel to the principal axis, then the value of d is
 

Options

A. 4 cm
B. 8 cm
C. 12 cm
D. 16 cm

Answer

C

Explanation

Image of lens will act as object for mirror.
Here, `v_(1)+u_(2)=40" cm"`
Lens formula, `(1)/(f_(1))=(1)/(u_(1))-(1)/(v_(1))`
Mirror formula, `(1)/(f_(2))=(1)/(u_(2))+(1)/(v_(2))`
For final image, `v_(2)=oo`
So, `(1)/(f_(2))=(1)/(u_(2))`
`implies" "u_(2)=15" cm"`
Now, `v_(1)=40-15=25" cm"`
So, value of `u_(1)` should be
`(1)/(20)=(1)/(u_(1))-(1)/(25)implies(1)/(u_(1))=(1)/(20)+(1)/(25)`
`implies" "u_(1)=100//9" cm"impliesu_(1)=1111" cm"`
= 12 cm (most near by answer)