A pole standing in a clear water pond stands `1m` above the water surface, the pond is `2m` deep. What are the lengths of the shadows thrown by the pole on the surface and bottom of the pond if the sun is `30^@` over the horizon? `(mu_(water)=4//3)`

Explanation

`1xxsin60'^@=musinr`
`(sqrt3)/(2)=4/3sinrimpliessin r =(3sqrt3)/(8)`

`x=sqrt(8^2-(3sqrt3)^2)=sqrt(64-27)=sqrt(37)`
`DeltaDEF`, `tanr=(3sqrt3)/(x)=(3sqrt3)/(sqrt37)=(EF)/(DE)=(EF)/(2)`
`EF=(6sqrt3)/(sqrt(37))`
`DeltaABD`, `tan60^@=(BD)/(AB)=(BD)/(1)impliesBD=sqrt(3)m`
Length of shadow on water surface.
`BD=sqrt3m`
Length of shadow on bottom of pond.
`CF=CE+EF=sqrt3+(6sqrt3)/(sqrt37)=sqrt3+sqrt3=2sqrt3m`