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A plane wavefront propagating from a rarer into a denser medium is incident at an angle of incidence i on a refracting surface. Draw a diagram showing incident wavefront and refractedwavefront . Hence verify Snell's laws of refraction. |
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Answer» Solution :Here `v_(1) and v_(2)` are speeds of light in medium 1 and 2 as shown BC= vt to get the shape of WAVE FRONT draw an arc of RADIUS `v_(2)t` form A towards medium 2. If CE is tangent PLANE then `AE=v_(2) t,` CE represents refracted wave front In `triangle ABC and triangle AEC sin i= (BC)/(AC)=(v_(1)t)/(AC) , sin r = (AE)/(AC) = (v_(2)t)/(AC)` So `(sin i)/(sin r)= (v_(1)t)/(cancel (AC))xx (cancel(AC))/(v_(2)t)=v_(1)/v_(2)` If c is speed of light in vaccum then `n_(1)=c/v_(1) and n_(2)= c/v_(2)"" rArr v_(1) =c/n_(1)and v_(2) =c/n_(2)` where `n_(1) and n_(2)` refractive indices of medium 1 and 2 `(sin i) /(sin r)=(c//n_(1))/(c//n_(2)) = n_(2)/n_(1)rArr""n_(1) sin i= n_(2) sin r` `rArr`Snell's law 
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