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

Options

A. `10 m s^(-1)`
B. `1 m s^(-1)`
C. `9 m s^(-1)`
D. `0.9 m s^(-1)`

Answer

B

Explanation

According to mirror formula, `(1)/(u)+(1)/(v)=(1)/(f)`
Diferentiating with respect to t, we get
`:. -(1)/(u^(2))(du)/(dt)-(1)/(v^(2))(dv)/(dt)=0` or `(dv)/(dt)=-((v)/(u))^(2)(du)/(dt)`
`v_(1)=-((v)/(u))^(2)v_(0)( :.(dv)/(dt)=v_(i) and (du)/(dt)=v_(0))`
Substituting the given values, we get
`v_(i)=-((10)/(30))^(2)xx9=-1 m s^(-1)implies|v_(i)|=1 m s^(-1)`