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, the apparent distance of the fly from the wall of the aquarium is `mux,` if x is the actual distance.
Then apparent velocity will be `d(mux)//dt rArr (v_("app"))_("fly")= muv_("fly")`
Now the fish observes the velocity of the fly to be `8ms^(-1)`
`rArr` Apparent relative belocity will be `= 8ms^(-1)`
`rArr v_("fish")+(v_("app"))_(" fly ")=8`
`3+muv_("fly")=8 rArr v_("fly" )=5xx3/4=3.75ms^(-1)`