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Prove laws of refraction using Hugyen's principle. |
Answer» Solution :Let us consider a PARALLEL beam of light is incident on a refracting plane surface XY such as a glass surface. The incident WAVEFRONT AB is in rarer medium (1) and the refracted wavefront A.B. is in denser medium (2). These wavefront are PERPENDICULAR to the incident rays L, M and refracted rays L.,M. respectively. By the time the point A of the incident wavefront touches the refracting surface, the point B is yet to travel a distance BB. to touch the refracting surface B..  `t=(BB.)/(v_(1))=(A A.)/(v_(2))(or)(BB.)/(A A.)=(v_(1))/(v_(2))` (i) The incident rays, the refracted rays and the normal are in the same plane. (ii) Angle of incidence, `i = angle NAL = 90^(@) - angle NAB = angle BAB.` Angle of refraction, `r = angle N.B.M. = 90^(@) - angle N.B.A = angle A.B.A.` For the two right angle triangles `Delta ABB. and Delta B.A.A`. `(sini)/(sinr)=(BB.//AB.)/(A A.//AB.)=(BB.)/(A A.) = (v_(1))/(v_(2))=(c//v_(2))/(c//v_(1))` Here, c is speed of light in vacuum. The ratio c/v is the constant, called REFRACTIVE index the medium. The refractive index of medium (1) is, `c//v_(1) = n_(1)` and the of medium (2) `c//v_(2) = n_(2)`. `(sini)/(sinr) = (n_(2))/(n_(1))` In product form, `n_(1) sin i = n_(2) sinr` Hence, the laws of refraction are proved. |
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