  Question

State Huygen's principle, Using this principle draw a diagram to show how a plane wave front incident at the interface of the two media gets refracted when it propagates from a rarer to a denser medium.Hence verify Snell's law of refraction .

Solution

Each point on the primary wave acts as a source of secondary wavelets. The new wavefront at any instant is the envelope of secondary wavelets at that instant.Time taken for light to go from Q to Q'$$t=\dfrac{QK}{c}+\dfrac{Q'K}{\nu}................(i)$$In right angled triangle $$\Delta AQK, \angle QAK=i$$$$\therefore QK=AKsin\ i............(ii)$$In right angled triangle $$\Delta P'Q'K, \angle Q'P'K=r$$ and $$Q'K=KP'sin \ r.................(iii)$$Using (i),(ii) and (iii) we get$$t=\dfrac{AKsin \ i}{c}+\dfrac{KP'sin \ r}{\nu}$$$$t=\dfrac{AKsin \ i}{c}+\dfrac{(AP'-AK)sin \ r}{\nu} (\because KP'=AP'-AK)$$$$t=\dfrac{AP'sin\ r}{\nu}+AK(\dfrac{sin\ i}{c}-\dfrac{sin \ r}{\nu})$$The incident rays will fall at the same time at corresponding points of the refracted wavefront if it is independent of AKi.e. $$\dfrac{sin \ i}{c}-\dfrac{sin \ r}{\nu}=0$$$$\dfrac{sin \ i}{sin \ r}=\dfrac{c}{\nu} \Rightarrow n=\dfrac{sin \ i}{sin \ r}$$ which is the Snell's Law for refraction of light.(b)(i) The frequency of incident,reflected and refracted light are all same as it only depends on the source of light.(ii)There is no reduction in energy since frequency remains constant. Physics

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