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What is Huygen's Principle? Explain the optical phenomenon of refraction using Huygen's principle. |
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Answer» Solution :HUYGEN's principle: Every point on a wave front is the source of SECONDARY wavelets. Refraction of a plane wave using Hyugen's principle. Let the surface PP' separating the two medium of rafractive index `mu_(1) and mu_(2)`. Let `v_(1) and v_(2)` be the velocities of light in medium 1 and medium 2. According to Huygen's principle every point on incident wave fron AB is a source of secondary wavelets. Byt the time wavelet from point B reaches at point C, the wavelet from point A would have rached at point E. Let t be the time taken from B to C is equal to time taken A to D. i.e, `i.e, t=(BC)/(v_(1))=(AE)/(v_(2)) Rightarrow (BC)/(AE)=(upsilon_(1))/(upsilon_(2))` .........(1) First law of refraction: `"In "Delta^(MU)ABC Rightarrow sin i=(BC)/(AC) RightarrowBC=AC sin i.....(2)` Similarly in `"In "Delta^(mu)ABC Rightarrow sin i=(BC)/(AC) RightarrowBC=AC sin i.....(2)` Dividing equation (2) by equation (3) `(BC)/(AE)=(upsilon_(1))/upsilon_(2)=(AC sin i)/(AC sin r)` `(v_(1))/(v_(2))=(sini)/(sin r) ({:(,mu_(1)=c/v_(1),mu_(2)=c/v_(2)),(,v_(1)=(c)/(mu_(1)),&v_(2)=c/mu_(2)):}) rArr c/mu_(1)xxmu_(2)/c=(sin i)/(sin r) therefore (mu=(sin i)/(sin r))` `mu_(1) sin i=mu_(2) sin r` This is the Snell's law of refraction. Second law of refraction: Since incident RAY, refracted ray, refracted ray and the normal all the lie on the same plane PP' at the point of incidence. This proves the second law of refractin. 
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