A convex mirror of focal length `10cm` is shown in figure. A linear object `AB=5cm` is placed along the optical axis. Point `B` is at distance `25cm` from the pole of mirror. The size of image of `AB` is

Options

A. `100/14` `cm`
B. `10/7` `cm`
C. `5/14` `cm`
D. none of these

Answer

C

Explanation

(c) For point `A,u=-25cm`
`f=+10cm`
`:.1/v+1/u=1/f`
or `1/v-1/25=1/10`
or `1/v=1/10+1/25` or `1/v=(5+2)/50`
`:.v=50/7=7.14cm`
For point `B,u'=-30cm`
`f'=10cm`
`1/(v')+1/(u')=1/(f')`
or `1/(v')-1/30=1/10` or `1/(v')=1/30+1/10=(1+3)/30=4/30`
`:. v'=30/4=7.5cm`
`:. A'B'=|v'-v|=|7.5-7.14|=0.36`