A person with normal eyesight can see visible light with wavelengths approximately in the range of $400 nm$ to $700 nm$ in air. A diver underwater, where the refractive index of water is $μ=\frac {4}{3}$, is shown a red warning light of wavelength $680 nm$ (in air) to alert him to a nearby danger. Will the diver be able to see the warning light as red? Justify your answer. [Note: A wavelength of $680 nm$ corresponds to red light in air, whereas $510 nm$ corresponds approximately to green light in air.]
Answer
The frequency $\nu = \frac {v}{\lambda}$
In water, the speed becomes $\frac {v}{\mu}$ and the wavelength becomes $\frac {\lambda}{\mu}$. So, the frequency does not change.
The colour depends on the frequency and therefore, red appears as red.
Although the wavelength in water is $λ_{water}=\frac {680}{4/3}=510 nm$,
this does not mean that the light becomes green. The value $510 nm$ corresponds to green light when the wavelength is specified in air, not when it is the wavelength of the same light in water. The calculated wavelength of $510 nm$ is a distractor if it is used to infer a change in colour.