The Brewster angle is the angle at which no reflection occurs in the medium of origin. It occurs when the incident angle $\theta_{B}$ is such that the reflection coefficient $\Gamma_{ \|}$ is equal to zero.The Brewster angle is given by the value of $\theta_{B}$ which satisfies

$$\sin \left(\theta_{B}\right)=\sqrt{\frac{\varepsilon_{1}}{\varepsilon_{1}+\varepsilon_{2}}}$$

For the case when the first medium is free space and the second medium has a relative permittivity $\varepsilon_{r},$The above equation can be expressed as

$$ \sin \left(\theta_{B}\right)=\frac{\sqrt{\varepsilon_{r}-1}}{\sqrt{\varepsilon_{r}^{2}-1}} $$

Note that the Brewster angle occurs only for vertical (i.e. parallel) polarization.