Question

A convex driving mirror of focal length `20cm`, is fitted in a motor car. If the second car `2m` broad and `1.6m` hight is `6m` away from first car and overtake the first car at a relative speed of `15m//s`, then how fast will the image he moving?
A. `0.016m//s`
B. `0.0257m//s`
C. `0.162cm`
D. `0.0073m//s`

Answer 1

(a) Mirror formula `1/v+1/u=1/f`
Differentiating w.r.t we get
`0=-1/(v^(2))(dv)/(dt)-1/(u^(2))(du)/(dt)`
`(du)/(dt)=-(v^(2))/(u^(2))(du)/(dt)`
But `(du)/(dt)=15m//s`
Now `1/v=(1/20+1/600)`
`:.v=600-31cm` and `v/u=(600/31)/600=1/31`
`:.` Speed of image `=(dv)/(dt)=-(1/31)^(2)xx16=0.016m//s`