A fish in an aquarium approaches the left wall at a rate of 2.5 m/s observes a fly approaching it at 8 m/s. If the refractive index of water is (4/3), find the actual velocity of the fly.

3.5m/s

For the fish the apparent distance of the fly from the wall of the aquarium is $μx$, if x is actual distance.

Then apparent velocity will be $\frac{d(μx)}{dt}$

$(v_{app})_{fly} = μ\, v_{fly}$

Now the fish observes the velocity of the fly to be 8 m/s

⇒ apparent relative velocity will be = 8 m/s

$v_{fish} + (v_{app})_{fly} = 8 m/s$

$⇒3 + μ\,v_{fly} = 8$

$v_{fly} = 5 ×\frac{3}{7} = 3.75 m/s$