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 ms^(-1)`
B. `1 ms^(-1)`
C. `9 ms^(-1)`
D. `0.9 ms^(-1)`

Answer

B

Explanation

Mirror formula, `1/u + 1/v = 1/f`
Differentiating with respect to t, we get
`:. - (1)/(u^(2)) (du)/(dt) - (1)/(v^(2)) (dv)/(dt) = 0`, ( ` :'` f is contant)
or `(dv)/(dt) = - (v/u)^(2) (du)/(dt)`
`v_(i) = -(v/u)^(2)v_(o)` , ( `:' (dv)/(dt)= v_(i)` and `(du)/(dt) = v_(o)`)
Substituting the given values, we get
`v_(i) = -(10/30)^(2) xx 9 = - 1 mx^(-1)` or `|v_(i)| = 1 ms^(-1)`