Water waves will change direction at a boundary between deep and shallow water. The waves slow down as they enter the shallow water which causes the wavelengths to shorten.
The density of a material affects the speed that a wave will be transmitted through it. In general, the denser the transparent material, the more slowly light travels through it. Glass is denser than air, so a light ray passing from air into glass slows down. If the ray meets the boundary at an angle to the normal , it bends towards the normal.
The reverse is also true. A light ray speeds up as it passes from glass into air, and bends away from the normal by the same angle. For a given frequency of light, the wavelength is proportional to the wave speed:. So if a wave slows down, its wavelength will decrease.
The effect of this can be shown using wave front diagrams, like the one below. The diagram shows that as a wave travels into a denser medium, such as water, it slows down and the wavelength decreases. Since amplitude is related to energy, when there is max amplitude going in, there is max amplitude going out, though the two maxima need not have the same value.
Also, we can directly say that, to conserve energy which is dependent solely on frequency , the frequency must remain constant. There doesn't seem to be any reason for the speed to change, as long as the energy associated with unit length of the wave decreases. It's like having a wide pipe with water flowing through it. The speed is slow, but there is a lot of mass being carried through the pipe. If we constrict the pipe, we get a jet of fast water. Here, there is less mass per unit length, but the speed is higher, so the net rate of transfer of mass is the same.
This is analogous to the pipe, where increase of speed required decrease of cross-section alternatively mass per unit length. Now we have established that speed can change, lets look at why. Now, an EM wave like light , carries alternating electric and magnetic fields with it. Here's an animation. Now, in any medium, the electric and magnetic fields are altered due to interaction with the medium. This means that the light wave is altered in some manner.
The energy of the light is related to the frequency; when the light enters the medium there are interference patterns that cause the apperent speed of light to change; if the frequency changed, the energy would not be conserved. The wavelength changes to balance the change in speed. Here is a slightly different take on this using the boundary conditions for electromagnetic fields at an interface. A key boundary condition, that is derived from Faraday's law, is that the component of the E-field tangential to the boundary must be continuous.
So take an EM wave travelling at normal incidence with the electric field solely in a direction tangential to the boundary. Given that the speed of light in a medium is changed for reasons explained in Manishearth's answer , then the wavelength of light in the medium must also change.
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Asked 9 years, 8 months ago. Active 7 years, 1 month ago. Viewed k times. The frequency of it has to stay the same?
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