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Question
Derive the law of reflection using Huygen’s Wave Theory.
Solution
Huygen’s wave theory :
Reflection at a plane surface : Consider a plane reflecting surface XY. Let AB be a plane wavefront of light incident obliquely on XY. When the incident wavefront touches XY at A, a secondary wavelet starts, spreading from A according to Huygens’ principle. Let the ray at B reach XY at D after a time t. If v is the speed of light in air then BD = vt. During this time t, the secondary wavelet from A spreads over a hemisphere of radius vt. with centre at A. Let CD be a tangent to this hemisphere. Then AC = BD. C and D are in the same phase. If we consider all the points between A and D, then CD will be tangential to all the secondary wavelets originating from these points at the end of t seconds. Hence CD is the reflected wavefront.
Draw AN normal to XY. Then
`anglePAN = i` , the angle of incidence , and `angleNAC = r` the angle of reflection
In triangles BAD and CDA
AC = BD = vt; AD is common, and `angleABD = angleACD = 90^circ` because the rays are normal to wavefronts.
`therefore` Triangles BAD and CDA are congruent
`therefore angleDAC = angleBDA , 90^circ - r = 90^circ - i`
OR `therefore i = r`
i.e , angle of incidence is equal to angle of reflection .
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