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State Huygens' principle and prove the laws of reflection on the basis of wave theory. |
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Answer» Solution :Laws of reflection (i) Ist Law. It STATES that angle of incidence is equal to angle of reflection. (ii) 2nd Law. It states that the incident ray, the reflected ray and the normal, at the point of incidence all lie in the same plane. First law of reflection. Let XY be a plane reflecting surface and AB be a plane wavefront incident on the surface as shown in the figure. According to Huygens. principle, every point on wavefront AB is a SOURCE of secondary WAVELETS and the time during which wavelet from B reaches at C, the reflected wavelet from A would arrive at D.  i.e. `t=(BC)/(v)=(AD)/(v)` or BC = AD, ...(i) where v is the velocity of light in the medium. In RT `/_ DeltaABC` , `sin i=(BC)/(AC)` or `BC = AC sin i` ...(ii) In rt `/_ Delta ADC, sin r=(AD)/(AC)` or AD = AC sin r ...(iii) Putting Eqs, (ii) and (iii) in (i), we get AC sin i =AC sin r or sin i = sin r or i = r i.e: Angle of incidence = angle of reflection This is first law of reflection. Second law of reflection. From the figure, we find that, the incident ray, the reflected ray and the normal all lie on the same plane XY. This proves second law of reflection. |
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