In the figure shown below, two objects A and B are placed one after another in front of a concave mirror of focal length 15 cm.

If the objects form image of same size, what should be the distance of object B from the mirror?

Explanation

Given, height of object, B = h
Height of object `A=2h`
Distance of object A from mirror, `u_(1)=-30cm`
Distance of object B from mirror, `u_(2)=?`
Focal length of mirror, `f=-15cm`
For object A :
`"Magnification, m"=(h_(2))/(2h)=(f)/(f-u_(1))`
For object B :
`"Magnfication, m."=(h._(2))/(h)=(f)/(f-u_(2))`
`rArr" "(m)/(m.)=(h_(2))/(2h)xx(h)/(h._(2))=(f-u_(2))/(f-u_(1))`
`"Given, "h._(2)=h_(2)`
`therefore" "(1)/(2)=(-15-u_(2))/(-15+30)`
`rArr" "15=-30-2u_(2)`
`rArr" "-45=2u_(2)rArr u_(2)=(-45)/(2)=-22.5cm`