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Physics Thus, if we wish to determine the shape of the wavefront at t = , we draw spheres of radius v from each point on the spherical wavefront where v represents the speed of the waves in the medium. If we now draw a common tangent to all these spheres, we obtain the new position of the wavefront at t = . The new wavefront shown as G G 1n2Fig. 10.2 is again spherical with point O as the centre. The above model has one shortcoming: we also have a backwave which is shown as D D in Fig. 10.2. Huygens argued that the amplitude of the secondary wavelets is maximum in the forward direction and zero in the backward direction; by making this adhoc assumption, Huygens could explain the absence of the backwave. However, this adhoc assumption is not satisfactory and the absence of the backwave is really justified from more rigorous wave theory. In a similar manner, we can use Huygens principle to determine the shape of the wavefront for a plane wave propagating through a medium FIGURE 10.3 (Fig. 10.3). Huygens geometrical construction for a 10.3 RE FR A CT IO N AND R EFLECTION OF plane wave propagating to the PL A NEW AVES U SIN GH UYGENS PR INC IPL E right. 1 F2is the 10.3.1 Refraction of a plane wave plane wavefront at t = 0 and G1G2is the We will now use Huygens principle to derive the laws of refraction. Let PP wavefront at a later represent the surface separating medium 1 and medium 2, as shown in time . The lines 1 2 ,Fig. 10.4. Let v1and v 2epresent the speed of light in medium 1 and B1B2… etc., are medium 2, respectively. We assume a plane wavefront AB propagating in normal to both F1F2 the direction A A incident on the interface at an angle i as shown in the and G 1 2nd represent rays. figure. Let be the time taken by the wavefront to travel the distance BC. Thus, BC = v 1 FIGURE 10.4 A plane wave AB is incident at an angle i on the surface PP separating medium 1 and medium 2. The plane wave undergoes refraction and CE represents the refracted wavefront. The figure corresponds to v2< v1so that the refracted waves bends towards the 258 normal. Reprint 2026-27