When an object is kept at a distance of 30 cm from a concave mirror, the image is formed at a distance of 10 cm from the mirror. If the object is moved with a speed of `9 cms^(-1)` , the speed ( in `cms^(-1)`) with which image moves at that instant is __________ .

Options

A. `0.1ms^(-1)`
B. `1ms^(-1)`
C. `3ms^(-1)`
D. `9ms^(-1)`

Answer

b.

Explanation

`(1)/(v)+(1)/(u)=(1)/(f)`
`-(du)/(u^(2))-(dv)/(v^(2))=0` or `-(dv)/(u^(2))-(du)/(v^(2))`
or `dv=-(v^(2))/(u^(2))du`
`=-(10xx10)/(30xx30)xx9ms^(-1)=-1ms^(-1)`