On the Basis of Huygens Wave Theory of Light, Show that Angle of Reflection is Equal To The Angle of Incidence. You Must Draw a Labelled Diagram for this Derivation - Physics (Theory)

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On the basis of Huygens Wave theory of light, show that angle of reflection is equal to the angle of incidence. You must draw a labelled diagram for this derivation

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Solution

Suppose that a plane wavefront of light is incident at a plane refracting surface MN. Let A1B1 and AB be the successive positions of the incident wavefront. A1A and B1B the corresponding rays. When the wavefront reaches the point A, it becomes a secondary source and emits secondary waves in the same medium. Let c be the speed of light in the medIum If t is the time taken by the incident ray to cover the distance BC, then, BC = c t. During this time, the secondary waves originating at A cover same distance c t in the same medium.Therefore, the secondary spherical wavelet has a radius c t.

With A as the centre, draw a hemisphere of radius ct in the same medium. It represents the secondary wavelet.
According to Huygens’s principle locus of the tangent to all secondary wavelets represent new wavefront. Draw
a tangent CD to the secondary wavelet. As the points C and D are in the same phase of wave motion, CD
represents the corresponding reflected rays. Wavefront in the medium. It moves parallel to itself, tackling successive
positions C1D1, C2D2 etc. AD2 and CC2 represent the corresponding reflected rays.

Proof: i be the angle of incidence and r be the angle of reflection.

From definition ∠BAC = i and ∠DCA = r

From Δ ABC and Δ BCA

BC = AD from construction

AC = AC common

`lfloorABC = lfloor ADC` right angles

Therefore Δ ABC and Δ DCA are congruent

∴ ∠BAC = ∠DCA 

∴ i = r

Hence laws of reflection is proved.

  Is there an error in this question or solution?
2014-2015 (March)

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