# What would be the material properties of a perfect reflector?

If I want to model a perfect reflecting material, what material parameters should I use? Specifically what refractive index or dielectric constant should I use?

I know from the Fresnel equations that a purely complex refractive index reflects 100% of the power, but in general it also adds a phase shift. What material parameters can give a reflection coefficient of exactly -1?

To the best of my knowledge an infinitely high refractive index of the reflecting medium can give the result I want, is there another way? I feel like I might be missing something simple.

Assuming normal incidence, the relations between reflected, transmitted and incident electric fields are \begin{align} E_{rs}&=\left(\frac{\eta_{c2}-\eta_{c1}}{\eta_{c2}+\eta_{c1}}\right)E_{is}\, , \tag{1}\\ E_{ts}&=\left(\frac{2\eta_{c2}}{\eta_{c2}+\eta_{c1}}\right)E_{is}\, \end{align} Strictly speaking, you cannot make (1) to be -1 but when the complex impedance $$\eta_{c1}$$ is much greater than $$\eta_{c2}$$ you reach nearly $$-1$$. The complex impedance for a good conductor is $$\sqrt{\frac{\mu\omega}{2\sigma}}\left(1+j\right)$$ and will go to $$0$$ in the limit of $$\sigma\to\infty$$, whereas the impedance of air is $$\approx 377\Omega$$. Thus, in going from air to a perfect conductor, (1) will reduce to $$E_{rs}=\left(\frac{\eta_{c2}-\eta_{c1}}{\eta_{c2}+\eta_{c1}}\right)E_{is} \approx \left(\frac{0-\eta_{c1}}{0+\eta_{c1}}\right)E_{is}\approx -E_{is}\, .$$