Question

A fish in an aquarium approaches the left wall at a rate of `3ms^(-1)` observes a fly approaching it at `8ms^(-1)`. If the refractive index of water is `(4//3)`, find the actual velocity of the fly.

Answer 1

For the fish, apparent distance of the fly from the wall of the aquarium is `mux`. If x is actual distance, then apparent velocity will be=`(d(mux))/(dt)`
`(v_(app))_(fly)=muv_(fly)`
Now, the fish observes the velocity of the fly to be 8 `ms^(-1)`
`rArr v_(fish)+(v_(app))_(fly)=8ms^(-1)rArr3+muv_(fly)=8`
`therefore` Velocity of fly `v_(fly)=5xx3/4=3.75ms^(-1)`