# Schlick's approximation

In 3D computer graphics, Schlick's approximation, named after Christophe Schlick, is a formula for approximating the contribution of the Fresnel factor in the specular reflection of light from a non-conducting interface (surface) between two media.

According to Schlick's model, the specular reflection coefficient R can be approximated by:

${\displaystyle R(\theta )=R_{0}+(1-R_{0})(1-\cos \theta )^{5}}$
${\displaystyle R_{0}=\left({\frac {n_{1}-n_{2}}{n_{1}+n_{2}}}\right)^{2}}$

where ${\displaystyle \theta }$ is the angle between the viewing direction and the half-angle direction, which is halfway between the incident light direction and the viewing direction, hence ${\displaystyle \cos \theta =(H\cdot V)}$. And ${\displaystyle n_{1},\,n_{2}}$ are the indices of refraction of the two medias at the interface and ${\displaystyle R_{0}}$ is the reflection coefficient for light incoming parallel to the normal (i.e., the value of the Fresnel term when ${\displaystyle \theta =0}$ or minimal reflection). In computer graphics, one of the interfaces is usually air, meaning that ${\displaystyle n_{1}}$ very well can be approximated as 1.