Total internal reflection and its applicationsHard

Critical Angle at Interface

At the interface between two materials having refractive indices n₁ and n₂, the critical angle for reflection of an em wave is θ_1C. The n₂material is replaced by another material having refractive index n₃, such that the critical angle at the interface between n₁ and n₃materials is θ_2C. If n₃ > n₂ > n₁; $\frac{{{n_2}}}{{{n_3}}} = \frac{2}{5}$ and $\sin {\theta _{2C}} - \sin {\theta _{1C}} = \frac{1}{2}$ , then θ_1C is :

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