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Two objects A and B when placed in turn ...

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

A

18 cm

B

15 cm

C

20 cm

D

25 cm

Text Solution

Verified by Experts

The correct Answer is:
B
Let `m_(A) = (I_(A))/(O_(A)) and m_(B) = (I_(B))/(O_(B))`
Here , `I_(A) = O_(A) and O_(A) = 3O_(B)`
`(m_(A))/(m_(B)) = (I_(A))/(O_(A)) xx (O_(B))/(O_(A)) = (I_(A))/(I_(B)) xx (O_(B))/(I_(B)) = (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) = - 15 cm`
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