Light velocity change in different medium

[timlee]

Hi,
As we know, "velocity = wavelength * frequency" and light will change its speed when it passes different types of medium.
I wonder in velocity, wavelength and frequency, which one's change cause the others changing? Does its frequency change in different types of medium? or its wavelength change?
Thanks!

 

[Yitzach]

Wavelength changes. If frequency changed, the wave on either side of the boundary would come out of phase and that makes no sense.

 

[timlee]

Thanks! Two questions:

in terms of cause and result, does the change in velocity cause the change in wavelength, or the reverse, or they are not directly of cause and result relation?

Is the conclusion same for other types of wave (general waves, not only light or electromagnetic field) passing different types of medium? i.e. frequency of wave does not change, but only wavelength and speed change.

 

[Yitzach]

The change in velocity of light is due to a change in permittivity (epsilon) and permeability (mu) of the medium. $$c^2=\frac{1}{\epsilon\mu}$$ for any medium. And $$299782458^2\frac{m^2}{s^2}=\frac{1}{\epsilon_0\mu_0}$$ for a vacuum. The change in velocity changes the wavelength.
The same is true for other waves like sound changing from air to steel. For sound, the parameters that change are "coefficient of stiffness" and density. "Coefficient of stiffness" depends on bulk modulus and shear modulus.
Earthquake waves do the same thing with changes in rock. See Wikipedia's article on the speed of sound.

If you want that simpler: "Changes in velocity are due to changes in medium parameters. Changes in wavelength are due to changes velocity. It applies to all wave phenomena."

 

[timlee]

Thank you!