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Use Huygen's principle to show how a plane wavefront propagates from a denser to rarer medium. Hence, verify snell's law of refraction. |
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Answer» Solution :Consider a plane surface XY separating a denser medium of refractive index `n_(1)` from a rarer medium of refractive index `n_(2)`. Let `c_(1) and c_(2)` be the values of SPEED of light in the two media, where `c_(2)gtc_(1)`. AB is a plane wavefront incident on XY at an angle `i`. Let at a given instant the end A of the wavefront just strikes the surface XY but the other end B has still to COVER a path BC. if it takes time `t`, then `BC=c_(1)t`. Meanwhile, point A begins to emit secondary wavelets which cover a DISTANCE `c_(2)t` in second medium in time t. draw a circular arc with a as centre and `c_(2)t` as radius and draw a tangent CD from point C o this arc. then CD is the refracted wavefront in the rarer medium which advances in the DIRECTION of rays 1.2.. the refracted wavefront subtends an angle r from surface XY. Now in `DeltaABC,sini=(BC)/(AC)=(c_(1)t)/(AC)`  and in `DeltaADC, sinr=(AD)/(AC)=(c_(2)t)/(AC)` `therefore (sini)/(sinr)=(c_(1)t//AC)/(c_(2)t//AC)=(c_(1))/(c_(2))=`a constant`=(n_(2))/(n_(1))=n_(21)`. Which is snell.s law of refractive. |
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