# Translations:Reflection and refraction – book/3/en

In Figure 12, *ST* is a plane interface (at right angles to the paper) separating two media. Line *PA* is perpendicular to this plane. Line *AD* is the trace (in the plane of the paper) of a plane wave at right angles to the paper and incident on the interface *ST* at the angle . Lines *EA* and *FB* are two parallel rays of the incident wave. At the instant that the point *A* on the incident wavefront strikes the interface *ST*, a wavelet is initiated, in accordance with Huygens’ principle. Similarly, a new wavelet is initiated at each successive point on *ST* as the incident wavefront *AD* advances and strikes *ST*. Finally, when point *D* strikes the interface *ST* at *B*, the wavelet *MCN*, with center at *A*, has the radius *AC = DB*. The radius of the wavelet at *B* at that particular instant is zero. Because the line *BC* is tangent to all the wavelets, it constitutes their envelope. Therefore, *BC* is a wavefront of the reflected wave. Because *BC* is tangent to the wavelet *MCN* at *C*, it follows that *BC* is perpendicular to the radius *AC*. Thus, *AG* is a reflected ray associated with the reflected wavefront *BC*. In addition, the right triangles *ABC* and *BAD* are similar, so that angle *ABC* equals angle *BAD*. But angle *ABC* equals angle , and angle *BAD* equals angle . Therefore, angle , the angle of reflection, equals angle , the angle of incidence.