Two objects `A` and `B` when placed in turn in front of a concave mirror of radius of curvature `15cm`, give images of equal size. If `A` is three times the size of `B` and is placed `30cm` from the mirror, the distance of `B` from the mirror is

Options

A. `18` cm
B. `15` cm
C. `20` cm
D. `25` cm

Answer

B

Explanation

Let `m_(A)=(I_(A))/(O_(A))` and `m_(B)=(I_(B))/(O_(B))`
Here, `I_(A)=I_(B)` and `O_(A)=3O_(B)`
`(m_(A))/(m_(B))=(I_(A))/(O_(A))xx(O_(B))/(I_(B))=(I_(A))/(I_(B))xx(O_(B))/(O_(A))=(1)/(3)`
Also, `m_(A)=(f)/(f-u_(A))` and `m_(B)=(f)/(f-u_(B))`
`:. (m_(A))/(m_(B))=((f-u_(B))/(f-u_(A)))` or `(1)/(3)=(-7.5-u_(B))/(-7.5-(-30))`
or `u_(B)=-15` cm