Example 11.1: Electromagnetic waves

Question: Consider electromagnetic waves of wavelength $\lambda = 30$cm in air. What is the frequency of such waves? If such waves pass from air into a block of quartz, for which $K=4.3$, what is their new speed, frequency, and wavelength?
 
Answer: Since, $f\,\lambda=c$, assuming that the dielectric constant of air is approximately unity, it follows that

$$f = \frac{c}{\lambda} = \frac{(3\times 10^8)}{(0.3)} = 1\times 10^9\,{\rm Hz}.$$

The new speed of the waves as they pass propagate through the quartz is

$$c' = \frac{c}{\sqrt{K}} = \frac{(3\times 10^8)}{\sqrt{4.3}} = 1.4\times 10^8\,{\rm m}\,{\rm s}^{-1}.$$

The frequency of electromagnetic waves does not change when the medium through which the waves are propagating changes. Since $c'=f\,\lambda$ for electromagnetic waves propagating through a dielectric medium, we have

$$\lambda_{\rm quartz} = \frac{c'}{f} = \frac{(1.4\times 10^8)} {(1\times 10^9)} = 14\,{\rm cm}.$$