An object O is located 40cm from the first of two thin converging lenses (each of focal length 20cm), as shown in the figure below. If speed of the right lens is `7cm//s` rightwards, speed of final image is `7x//4cm//s` at the instant shown, find the value of x.

Answer

3

Explanation

From first lens
`x=-40cm`
`V=40cm`
For second lens
`u=20cm`
`V=10cm`
`(dV)/(dt)=((V)/(u))^(2)((du)/(dt))`
`V_(I//L)=((10)/(20))^(2)V_(0//L)`
`(V_(I)-V_(L))=(1)/(4)(V_(0)-V_(L))`
`(V_(I)-7)=-(7)/(4)`
`V_(I)=(21)/(4)`
`x=3`