Правка разделов «Statement», «Solution», «Answer»
en/12.2.2.md
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| @@ -1,11 +1,22 @@ | |||
| ### Statement | |||
| − | $12.2.2.$ [Insert the problem statement] | ||
| + | $12.2.2$. How do the wavelength and wave speed change when a wave transitions into a medium with refractive index $n$? Does the frequency of the wave change? | ||
| ### Solution | |||
| + | It is known that the refractive index determines the change in the speed of light in a medium compared to a vacuum. Therefore, by definition | ||
| + | $$ | ||
| + | c' = \frac{c}{n} | ||
| + | $$ | ||
| + | We also know that the energy of a photon is given by $E = h\nu$; this energy does not change when transitioning into another medium, so the frequency $\nu$ also does not change. | ||
| − | $12.2.2$. How do the wavelength and wave speed change when a wave transitions into a medium with refractive index $n$? Does the frequency of the wave change? | ||
| + | The wavelength is then defined as: | ||
| + | $$ | ||
| + | \lambda = \frac{c'}{\nu} = \frac{\lambda}{n} | ||
| + | $$ | ||
| + | |||
| #### Answer | |||
| − | [Insert a concise answer or boxed result] | ||
| + | $$ | ||
| + | \boxed{c'=\frac{c}{n};\quad \lambda=\frac{\lambda}{n};\quad \nu=const} | ||
| + | $$ | ||
| @@ -1,11 +1,22 @@ | |||
| ### Statement | ### Statement | ||
| $12.2.2.$ [Insert the problem statement] | $12.2.2$. How do the wavelength and wave speed change when a wave transitions into a medium with refractive index $n$? Does the frequency of the wave change? | ||
| ### Solution | ### Solution | ||
| It is known that the refractive index determines the change in the speed of light in a medium compared to a vacuum. Therefore, by definition | |||
| $$ | |||
| c' = \frac{c}{n} | |||
| $$ | |||
| We also know that the energy of a photon is given by $E = h\nu$; this energy does not change when transitioning into another medium, so the frequency $\nu$ also does not change. | |||
| $12.2.2$. How do the wavelength and wave speed change when a wave transitions into a medium with refractive index $n$? Does the frequency of the wave change? | The wavelength is then defined as: | ||
| $$ | |||
| \lambda = \frac{c'}{\nu} = \frac{\lambda}{n} | |||
| $$ | |||
| #### Answer | #### Answer | ||
| [Insert a concise answer or boxed result] | $$ | ||
| \boxed{c'=\frac{c}{n};\quad \lambda=\frac{\lambda}{n};\quad \nu=const} | |||
| $$ | |||