Speed, Frequency and Wavelength of light in Different Media

In different matrials, light travels at different speeds,
Because the speed of light,  
\[c\]
  the frequency  
\[f\]
  and the wavelength  
\[\lambda\]
  are related by the equation  
\[c = f \lambda\]
  it might be throught that the frequency and wavelength both change but this is not the case.
In air the speed is  
\[c\]
  , the frequency is  
\[f\]
  and the wavelength is  
\[ \lambda\]

In medium 1 with refractive index  
\[n_1\]
  the speed is  
\[\frac{c}{n_1}\]
  , the frequency is  
\[f\]
  and the wavelength is  
\[\frac{ \lambda}{n_1}\]

The wave equation  
\[c=f \lambda\]
  becomes  
\[\frac{c}{n_1}=f \frac{\lambda}{n_1}\]
 
We can muliply by  
\[n_1\]
  on both sides to get  
\[c = f \lambda\]

If the light then travels through medium 2 with refractive index  
\[n_2\]
  the speed is  
\[\frac{c}{n_2}\]
  , the frequency is  
\[f\]
  and the wavelength is  
\[\frac{ \lambda}{n_2}\]

The wave equation  
\[c=f \lambda\]
  becomes  
\[\frac{c}{n_2}=f \frac{\lambda}{n_2}\]
 
We can muliply by  
\[n_2\]
  on both sides to get  
\[c = f \lambda\]

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