Question

Two object `A` and `B` when placed in turns infront of a concave mirror, give images of equal size. The focal length of the concave mirror is `7.5cm` and size of object `A` is three times the size of object `B` from the mirror , if `A` is placed `30cm` from the mirror.
A. `18cm`
B. `15cm`
C. `20cm`
D. `25cm`

Answer 1

(b) Let `m_(A)=(l_(A))/(O_(A))` and `m_(B)=(l_(B))/(O_(B))`
Here `l_(A)=O_(A)` and `O_(A)=3O_(B)`
`(m_(A))/(m_(B))=(l_(A))/(O_(A))xx(O_(B))/(l_(B))=(l_(A))/(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)))`
`1/3=(-7.5-u_(B))/(-7.5-(-30))`
`u_(B)=-15cm`