Along the main optical axis of a converging lens with focal length F = 5 cm two fireflies are moving towards each other. They are on opposite sides of the lens. The speed of the fireflies is the same `V=2 cm//sec` After what minimum time (in sec) does the first firefly meet the image of the second, if at the initial time they were at distances 20 cm and 30 cm from the lens repectively? Round off to nearest integer.

Answer

`0006`

Explanation

`u=-(30-2t)`
`v=20-2t`
`1/v-1/u=1/F`
`1/(20-2t)+1/(30-2t)=1/5`
`(50-4t)/(600+4t^(2)-100t)=1/5`
`250-20=600+4t^(2)-100t`
`4t^(2)-80t+350=0`
`t=(40pmsqrt(1600-1400))/4= (40-14)/4=6.465 sec`