The speed at which the image of the luminous point object is moving, if the luminous point object is moving at speed ` v_(0)` towards a spherical mirror, along its axis is
(Given, `R=` radius of curvature `u=` object distance)

Options

A. `v_(i)=-v_(0)`
B. `v_(i)=-v_(0)((R)/(2u-R))`
C. `v_(i)=-v_(0)((2u-R)/(R))`
D. `v_(i)=-v_(0)((R)/(2u-R))^(2)`

Answer

D

Explanation

`(1)/(v)+(1)/(u)=(1)/(f)`
Differentiating both sides, `(-1)/(v^(2))(dv)/(dt)=(1)/(u^(2))(du)/(dt)`
`:. (dv)/(dt)=v_(1)=-((v)/(u))^(2)(du)/(dt)=-((v)/(u))^(2)v_(0)`
Again `(1)/(v)=(1)/(f)-(1)/(u)=(2)/(R)-(1)/(u)=(2u-R)/(Ru)[:. f=(R)/(2)]`
or `v=(uR)/(2u-R)`
`:. v_(i)=-((v)/(u))^(2)v_(0)` or `v_(i)=-v_(0)((R)/(2u-R))^(2)`