Reflection-Wave Theory
According to Huygens principle, every point on AB is a source of secondary wavelets. Let the secondary wavelets from B strike M1M2 at A’ in t seconds.
Therefore,BA’ = c × t (1)
Where c is the velocity of light in the medium, the secondary wavelets from A will travel the same distancec × tin the same time. Therefore, with A as the centre andc × tas radius, draw an arc B’ so that
AB’ = c × t (2)
From A’ draw a tangent plane A’B’ touching the spherical arc tangentially at B’. Therefore, A’B’ is the secondary wavefront after t seconds. This would advance in the direction of rays1’, 2’, 3’,which are the corresponding reflected rays perpendicular to A’B’.
For A’B’ to be true reflected wavefront, secondary wavelets starting from any other point D on the incident wavefront AB, must reach the point D’ on A’B’, after reflection at P, and that too, in the same time as the secondary wavelets take to go from B to A’. For this,
DP + PD’ = BA’ (1)
To prove it, drawPN ⊥ BA’
Therefore,DP = BN
InΔs ABA’ and AB’A’ = 90°
And AA’ is common, therefore Δs are congruent.
Therefore,∠BAA ' =∠B萨那(2)
AsPN || AB, therefore,∠ BAA’ = ∠NPA’ (3)
From (2) and (3),
∠BAA ' =∠B萨那
= ∠D’A’P +∠ NPA’ (4)
Now, inΔs NPA’andD’PA’
∠NPA’ = ∠D’PA” (already proved)
∠PNA’ = ∠PD’A’ = 90°andPA’是常见的。
Therefore,Δsare congruent.
Therefore,NA’ = PD’
As DP = BN, therefore,
BN + NA’ = DP + PD’
或BA’ = DP + PD’which is the necessary condition as per eqn. (1).
Hence, A’B’ is the true reflected wavefront. In fig.
Angle of incident,i = ∠B’AA’
And angle of reflection,r = ∠B’A’A
From (2),∠B’AA’ = ∠B’A’Ai.e.i = r, which is the law of reflection.
Further, the incident wavefront AB, the reflecting surfaceM1M2and the reflected wavefront A’B’ are the perpendicular to the plane of the paper. Therefore, incident ray, normal to the mirrorM1M2and reflected ray all lie in the plane of the paper. This is the second law of reflection.
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