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_(l)=-v_(o)`
B. `v_(l)=-v_(o)[R/(2u-R)]^(2)`
C. `v_(l)=-v_(o)((2u-R)/R)`
D. `v_(l)=-v_(o)(R/(2u-R))`

Explanation

(c) `1/v+1/u=1/f`
Differentiating both sides `-1/(v^(2)) (dv)/(dt)=1/(u^(2))(du)/(dt)`
`(dv)/(dt)=v_(l)=-(v/u)^(2)(du)/(dt)=-(v/u)^(2)v_(0)`
Again `1/v=1/f-1/u=2/R-1/u=(2u-R)/(Ru)`
`v=(uR)/(2u-R)`
`v_(i)=-(v/u)^(2)v_(o)=-v_(o)(R/(2r-R))^(2)`