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State Huygen's principle for the propagation of light and prove the laws of refraction of light on its basis. |
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Answer» Solution :Huygen.s Principle. Huygens principle helps to find the new position and shape of wavefront at any INSTANT of time, if the wavelength of earlier time is known. It is based on the following two assumptions : 1. All the particles on a wavefront can be regarded as point sources of new disturbance called the secondary wavelets which travel out with the same velocity as that of the ORIGINAL waves, provided the medium is the same. 2. A surface tangential to the secondary wavelets gives the position and shape of the new wavefront. Laws of refraction Let XY be a plane refracting surface separating two media of refractive index `mu_1 and mu_2` respectively. Let the velocity of light in medium of refractive index `mu_1` be `v_1` and that in medium of refractive index `mu_2 be v_2`. (It is assumed that `mu_2 gt mu_1` and hence `v_1 gt v_2`). FIRST law of refraction Let a plane wavefront AB incident on XY at an angle i. According to Huygens principle each point on the wavefront becomes a source of secondary wavelets and Time taken by wavelets from B to C = time taken by Wavelets from A to D.  i.e., `t = (BC)/v_1 = (AD)/v_2` `or (BC)/(AD) = v_1/(v_2)`...(i) Inrt. `angle DeltaABC` `(BC)/(AC) = sin i` `or BC = AC sini` `or BC = AC sin i` ...(ii) Similarly, in rt. `angle DeltaADC` `AD = AC sin r`...(iii) From (ii) and (iii), we have `(BC)/(AD) = (sin i)/ (sin r)`...(iv) From (i) and (iii),we have `(sin i)/(SINR) = v_1/v_2 = ""^1mu_2` This is first law of refraction and is called Snell.s law. Second law of refraction. Since the incident ray, refracted ray and the normal, all lie on the same plane XY at the point of incidence. This proves second law of refraction. |
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