Abeam of monochromatic light with a wavelength of 400 nm in air travels into water. what is the wavelength of the light in water? give your answer in nanometers.

The refractive index of water is . This means that the speed of the light in the water is:


The relationship between frequency f and wavelength  of a wave is given by:

where v is the speed of the wave in the medium. The frequency of the light does not change when it moves from one medium to the other one, so we can compute the ratio between the wavelength of the light in water  to that in air  as

where v is the speed of light in water and c is the speed of light in air. Re-arranging this formula and by using , we find

which is the wavelength of light in water.