A stationary observer O looking at a fish (in water of `mu=4//3` ) through a converging lens of focal length `90.0cm. ` the lens is allowed to falll freely from a height of `62.0cm` with its axis vertical. The fish and the observer are on the principal axis of the lens. The fish moves up with constant velocity `100cm s^(-1)` . Initially, it was at a depth of `44.00cm. ` Finally the velocity with which the fish appears to move to the observer at `t=0.2sec. `

Answer

22

Explanation

At `t=0.2 sec` , velocity of lens
`V_(l)=gt=2m//s` (downwards)
`therefore` For lens the fish appears to approach with a speed of `2+(1xx(3)/(4))=(11)/(4)m//s`
at a distance of `(42+(24)/((4/3)))=60 cm `

`therefore` distance of image from lens, `V=(-60xx90)/(-60+90)=-180 cm` .
`therefore` Velocity of image `w.r.t` . lens `V_(i)=(v^(2)/(u^(2)))(du)/(dt)=((-180)/(-60))^(2)xx(11)/(4)=(99)/(4)m//s`
velocity of image `w.r.t`. observer `=V_(i)-2=(99)/(4)-2(91)/(4)m//s=22.75 m//s` (upwards)