Question 80 of 295

At the interface between two materials having refractive indices \(n_1\) and \(n_2\), the critical angle for reflection of an em wave is \(\theta_{1 C}\). The \(n_2\) material is replaced by another material having refractive index \(n_3\) such that the critical angle at the interface between \(n_1\) and \(n_3\) materials is \(\theta_{2 \mathrm{C}}\). If \(\mathrm{n}_3\gt\mathrm{n}_2\gt\mathrm{n}_1 ; \frac{\mathrm{n}_2}{\mathrm{n}_3}=\frac{2}{5}\) and \(\sin \theta_{2 \mathrm{C}}-\sin \theta_{1 \mathrm{C}}=\frac{1}{2}\), then \(\theta_{1 \mathrm{C}}\) is