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I have two question about light:

  1. When a light wave travels from free space to a medium then there is a change in the amplitude. Why?

  2. when a wave changes its medium then its frequency does not change but wavelength changes. Why?

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  1. The change in the amplitude of the light wave is due to the reflection of the wave at the boundary. The sum of amplitudes of the reflected and transmitted wave is equal to the amplitude of the incident wave.

  2. The wavelength changes because the change in the medium usually means a change in refractive index $n$. The phase velocity $v$ of the wave is $v=c/n$ where c is the speed of light in vacuum. Therefore, when the wavelength in medium 1 is $\lambda_1=c/n_1$, the wavelength in medium 2 will be $\lambda_2=c/n_2$. Thus $$\lambda_1/\lambda_2=n_2/n_1$$

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  • $\begingroup$ As to why the wavelength changes, but the frequency does not, one could add the conservation of energy. $\endgroup$ – noah Jan 13 '18 at 3:03
  • $\begingroup$ That the frequency doesn't change is a consequence of the electromagnetic wave theory. $\endgroup$ – freecharly Jan 13 '18 at 3:09
  • $\begingroup$ If you want to see it this way it is a fundamental property of any wave, but OP specifically asked for it, so some explanation should be contained in the answer. $\endgroup$ – noah Jan 13 '18 at 3:13
  • $\begingroup$ How this can be explained by conservation of energy $\endgroup$ – Keshav Jan 13 '18 at 5:50
  • $\begingroup$ @keshav - In electromagnetic wave theory the conservation of energy is described by the Poynting Theorem (en.wikipedia.org/wiki/Poynting%27s_theorem) relating energy density and energy flux which is consistent with the reflection/transmission of the light wave. $\endgroup$ – freecharly Jan 13 '18 at 15:00

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