# 10.6: Example- Copper

- Page ID
- 22725

The real and imaginary parts \(\left(\mathrm{n}_{\theta}+i \kappa_{\theta}\right)=\sqrt{\epsilon_{\mathrm{r}}-\sin ^{2} \theta}\) have been plotted in Figure (10.6.8) as a function of the angle of incidence, θ, for room temperature copper and for a wavelength of λ= 0.5145 microns (see Table(10.1)). As can be seen from the figure, the angular dependence of the indices n_{θ}, \(\kappa\)_{θ} is not very pronounced. For a lossy material such as copper that has a complex dielectric constant the reflectivity, E_{R}/E_{0}, is complex; that is, the phase shift between the incident wave and reflected wave electric vectors is neither 0^{◦} (in phase) nor 180^{◦} (out of phase). The real and imaginary parts of the reflectivity have been plotted in Figure (10.6.9) as a function of the angle of incidence for S-polarized 0.5145 micron light incident on room temperature copper; the absolute value of the reflectivity has been plotted in Figure (10.6.10).

Similarly, the real and the imaginary parts of the ratio H_{R}/H_{0} have been plotted in Figure (10.6.11) as a function of the angle of incidence for P-polarized 0.5145 micron light incident on copper; the absolute value of this ratio is shown in Figure (10.6.12). The reflection coefficient for P-polarized radiation is given by R_{P} = E_{R}/E_{0} but this is very closely related to the ratio H_{R}/H_{0 }because E_{0} = Z_{0}H_{0} and E_{R} = −Z_{0}H_{R}, where Z_{0}= 377 Ohms, the impedance of free space. Notice that the real part of the reflectivity for P-polarized light vanishes at an angle of incidence of approximately 69^{◦} ; the phase of the reflected light at that angle is shifted by 90^{◦} relative to the incident light. The phase shift between reflected and incident light is much less pronounced for S-polarized light; approximately 15^{◦} for an angle of incidence of 69^{◦} .