Focal length of the convex lens shown in figure is `20cm.` Find the image position and image velocity.

Explanation

For the given condition,
`u=-30cm,` `f=+20cm`
Using the lens formula,we have
`1/v-1/-30=(1)/(+20)`
Solving this equation, we get
`v=+60cm` and
`m=v/u=+60/-30=-2`
`m^2=4`
Component of velocity of object along the axis `=5cos37^@=4mm//s` (towards the lens)
component of velocity of image along the axis `=m^2(4mm//s)=4xx4=16mm//s.` This
component is away from the lens (in the same direction of object velocity component)
Component of velocity of object perpendicular to the axis `=5sin37^@=3mm//s` (upwords).
`:.` Component of velocity of image perpendicular to axis `=m(3mm//s) or (-2)(3mm//s)`
`=-6mm/s or this component is ` 6mm//s` downwards. These all points are shown in the figure
given below.

`v_I =sqrt((16)^2+(6)^(2))`
`=sqrt(292)mm//s`
`tan theta=6/16=3/8`
or `theta= tan^(-1)(3//8)`