CBSE Class 10 Answered
explain huyguns principle and prove of snells law? briefly
Asked by ujjwalviky2003 | 11 Jun, 2018, 04:32: PM
Expert Answer
If we have a point source emitting waves uniformly in all directions, then the locus of points which have same amplitude and vibrates in same phase are spheres and we have what is know as spherical waves. At a large distance from the source, a small portion of sphere can be considered as a plane wave. Wavefront is defined as a wave surface of constant phase. At any instant, all points on the wavefront are oscillating in phase.
According to Hygenes principle, each point of wave front is the source of secondary dsturbance and the wavelets emanating from these points spread out in all diretions with the speed of waves. These wavelets emanating from the wavefront are usually refereed to as secondary wavelets and if we draw a common tangent to all the spheres, we obtain the new position of the wavefront at a later time.
Let PP' represent the surface separating medium-1 and medium-2 as shown in figure. Let v1 and v2 represent the speed of light in medium-1 and medium-2 respectively. We assume a plane wavefront AB propagating in the direction AA'incident on the interface at an angle i as shown in figure. Let τ be the time taken by the wavefront to travel the distance BC. Then BC = v1τ.
In order to determine the shape of the refracted wavefront, we draw a sphere of radius v2τ from the point A in second media. (speed of wave in 2nd medium is v2). Let CE represent a tangent plane drawn from the point C on the sphere. Then AE = v2τ and CE would represent the refracted wavefront. If we now consider the triangles ABC and AEC, we obtain
sin i = BC/AC = v1τ/AC and sin r = AE/AC = v2τ/AC
i and r are angle of incidence and angle of refraction respectively. then sin i / sin r = v1 / v2
Noe if c is speed of light in vacuum, then n1 = c/v1 and n2 = c/v2, where n1 and n2 are refractive indices of medium-1 and medium-2 respectively.
in terms of refractive indices above equation can be written as n1× sin i = n2× sin r
this is snell's law of refraction
Answered by Thiyagarajan K | 13 Jun, 2018, 04:22: PM
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