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. Calculate the size of the image of AB.

Explanation

For point B, `u=-25 cm, 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)`
For point A,` u^(')=-30 cm ` and `f^(')=10 cm`
`(1)/(v^('))+(1)/(u^('))=(1)/(f^(')) or (1)/(v^('))-(1)/(30)=(1)/(10)`
or `(1)/(v^('))=(1)/(30)+(1)/(10)=(1+3)/(300)=(4)/(30)`
`:. v^(')=(30)/(4)=(15)/(2) cm`
`:. A^(')B^(') =(15)/(2)-(50)/(7)=(5)/(14)cm`