Question

An object is approaching a convex lens of focal length 0.3m with a speed of `0.01m s^(-1)`. Find the magnitudes of the ratio of change of position and lateral magnification of image when the object is at a distance of 0.4m from the lens

Answer 1

Correct Answer - `0.09m//s;Magnitude of the rate of change of lateral magnification is`0.3s^(-1)`
(i)`(1)/(v)-(1)/(u)=(1)/(f)`
differentiating the equation with respect to time
`-(1)/(v^(2))(dv)/(dt)+(1)/(u^(2)).(du)/(dt)=0 rArr (dv)/(dt)=((v)/(u))^(2) .(du)/(dt)….(1)`
`(dv)/(dt)=((f)/(f+u))^(2).(du)/(dt) rArr (dv)/(dt)=((0.3)/(0.3-0.4))^(2)xx0.01m//s`
`=9xx0.01m//s`
`(dv)/(dt)=.9m//s`
(ii)`m_t=v/u=f(f+u) implies (dm)/(dt)=d/(dt)(f+(f+u)) (dm)/(dt)=f/(f+u)^2 (du)/(dt)`
`implies (dm)/(dt)=- 0.3/(-0.4+0.3)^2 xx.01`