The focal length of a convex lens is 15 cm, and an object initially placed at a distance 30 cm starts moving away from the lens at speed 2.5 cm/s. Find the speed of image in cm/s towards the lens at that very instant.

Answer

`10.00`

Explanation

From lens formula,
`1/f =1/v-1/u` ...(i)
`:. 1/v = 1/15 + (1)/(-30)=1/30`
`:. v = 30cm`
Now differentiating equation (i), `0=-1/v^2(dv)/(dt)-(-1/u^2)(du)/(dt).....` ( `:.` f is constant )
`:. 1/v^2 xx(dv)/(dt) =1/u^2xx(du)/(dt)`
`:. (1/30)^2 xx(dv)/(dt)=(1/(-15))^2 xx(2.5)`
`:. (dv)/(dt) = (30/-15)^2 xx2.5 = ` 10 cm/s