Answer to Question #249018 in Optics for Philasande

Question

A prism has a refracting angle of 60 degrees and a refractive index of 1.60. calculate the angle of incidence on the first face for a ray that is just totally reflected at the second face of the prism

Answer 1

$$\theta_c=\arcsin\frac{n_1}{n_2}=38.7°.$$

From the diagram, find the angle of refraction:

$$\theta_r=60°-\theta_c=21.3°.$$

Apply Snell's law:

$$\frac{\sin\theta}{\sin\theta_r}=\frac{n_2}{n_1},\\\space\\ \theta=\arcsin\bigg(\sin\theta_r·\frac{n_2}{n_1}\bigg)=35.5°.$$