When light travels from air to water ,why there is change in wavelength but not frequency

firstly the speed of light in any medium is v = 1/sq.rt(mu . epsilon) which is what james clerk maxwell proved. So if both mu and epsilon change when light enters water ... the speed of light should change. This takes care of the question as to why the speed should change. Now consider a light wave, with say 10 vibrations per second. There is no reason as to why the number of vibrations in air should change when light enters water. Say if light has to lose energy, it should lose amplitude. So the number of vibration must remain constant but since speed of light in medium = frequency . wavelength ...and since speed and frequency don't change therefore wavelength changes. Yet another way of looking at it is through experiment. "The color of light is not primarily dependent on the wavelength of the light, as most people probably think. A wavelength of 389 nm is violet light in a vacuum, where the index of refraction is 1.000. However, in a medium where the index of refraction is greater than 1.000, the wavelength of violet light is not necessarily exactly 389 nm. The color mainly is dependent upon the light's frequency, which is the number of waves of the light that pass a given point in one second. If the color of light was dependent on wavelength, its color would change when it entered a medium with a different index of refraction. But it doesn't. For instance, if you look at an object in air, and then jump into a swimming pool with the object and look at it under water, the color of the object will remain the same." source: http://www.tedmontgomery.com/remarks%5C08.1-12/optics/index.html Also there is a theoretical derivation as to why this happens which depends on solving maxwells equations at the boundary with boudary conditions such that the intensity of light in air equals the sum of intensities of light which is reflected and refracted at the interface. The result of solving with such boundary conditions is that we get a change on wavelength but not frequency. I hope this suffices Cheers read less