Wave Optics

Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are 2.8 (medium \(-1\)) and 6.8 (medium \(-2\)), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be \({\tan ^{ - 1}}{\left( {1 + {{10} \over \theta }} \right)^{{1 \over 2}}}\) the value of \(\theta\) is __________.

(Given for dielectric media, \(\mu_r=1\))