A real object is placed infront of a convex mirror (focal length f). It moves towards the mirror, the image also moves. If `V_(i)=` speed of image and `V_(0)=` speed of the object and u is the distance of object from mirror along principal axis, then

Options

A. `V_(i) lt V_(0)` if `|u| lt |f|`
B. `V_(i) gt V_(0)` if `|u| gt |f|`
C. `V_(i) lt V_(0)` if `|u|gt|f|`
D. `V_(i)=V_(0)` if `|u|=|f|`

Answer

a.,c.

Explanation

`(1)/(v)+(1)/(-u)=(1)/(f)rArrv=(uf)/(u+f)`" "vltu` and `v lt f`
`V_(0)=-(du)/(dt),V_(I)=-(dv)/(dt)`
Differentiating `(1)/(v)-(1)/(u)=(1)/(f)`
`rArr -(1)/(v^(2))(dv)/(dt)+(1)/(u^(2))(du)/(dt)=0`
`rArr -(1)/(v^(2))(-V_(i))+(1)/(u^(2))[-V_(0)]=0rArr V_(i)=((v)/(u))^(2)V_(0)`
Since `V lt u` so `V_(i) lt V_(0)` for each case.