Light and optics: An experiment with light rays and a prism

A student is conducting an experiment to explore the angles made by reflected and refracted light. To do this the student uses a laser to fire a ray of light toward a rectangular prism that has an index of refraction of n${}_{\text{p}}$‍. The laser light first strikes the surface of the prism at an angle θ${}_{\text{1}}$‍. Some of the light is reflected off of the front diagonal surface of the prism. The rest of the light is refracted through the prism at an angle θ${}_{\text{3}}$‍. This refracted light makes its way to the backside of the prism at an angle θ${}_{\text{4}}$‍ and is refracted once more from the prism into the air at an angle of θ${}_{\text{5}}$‍. This process is represented in the diagram below. Dotted lines are not part of the experiment and are shown in the diagram for reference purposes only. The right angle symbol is used to represent angles of 90${}^{\circ }$‍. Angles shown in the diagram are not necessarily drawn exactly to proportion.