# How is full reflection (mirror) compatible with the fresnel equations

I'm working on a raytracer with realistic material properties and I am using the Fresnel Equations to calculate the chance of a ray being reflected or refracted on a material boundry. It seems though that the reflectivity does not behave as expected. I have created a sphere with the index of refraction of mercury and it pretty much has the same reflective properties as a parafin or plastic object. I would have expected near-full reflectivity here. Is there more to reflection than the fresnel equations ?

• The Fresnel equations tell you how much light passes through and how much is reflected. But it does not tell you have specular/diffuse the surface is. Aug 26, 2016 at 9:59

For metals, the index of refraction is a complex number. The Fresnel equations remain valid when the index is complex: $n_\mathrm{complex}=n + ik$.

Using only the real part only is not adequate. Both values for Mercury, and many other materials can be found on this very useful website. Lower down on that page you will see the results for transmission and reflection of Mercury, and you will see that they do not resemble paraffin.

• Uh, I didn't know that. Is it possible to adapt Schlick's approximation for complex numbers ?
– fis
Aug 26, 2016 at 12:49
• Sorry, I can't help you there. You might ask at a forum more closely related to computer graphics. Aug 26, 2016 at 12:54
• Okay I might. One last question: Could I use the regular Fresnel Equations and just use complex numbers instead of the ior ?
– fis
Aug 26, 2016 at 13:01
• Yes, you can ... but what is "ior"? Is that a typo? Aug 26, 2016 at 13:03
• Index of refraction
– fis
Aug 26, 2016 at 13:04