P RINCIPLE

P RINCIPLE . . Refraction of a plane wave We will now use Huygens principle to derive the laws of refraction. Let PP represent the surface separating medium and medium , as shown in Fig. . . Let v and v represent the speed of light in medium and medium , respectively. We assume a plane wavefront AB propagating in the direction A A incident on the interface at an angle i as shown in the figure. Let * be the time taken by the wavefront to travel the distance BC. Thus, BC = v * In order to determine the shape of the refracted wavefront, we draw a sphere of radius v * from the point A in the second medium (the speed of the wave in the second medium is v ). Let CE represent a tangent plane drawn from the point C on to the sphere. Then, AE = v * and CE would represent the refracted wavefront. If we now consider the triangles ABC and AEC, we readily obtain sin i = BC AC AC v ( . ) and sin r = AE AC AC v ( . ) where i and r are the angles of incidence and refraction, respectively. FIGURE . A plane wave AB is incident at an angle i on the surface PP s eparating medium and medium . The plane wave undergoes refraction and CE represents the refracted wavefront. The figure corresponds to v < v so that the refracted waves bends towards the normal.