We can prove the laws of reflection on the basis of Huygens’s wave theory as follows:
In the given figure, AB is the wavefront incident on a reflecting surface XY with an angle of incidence i as shown in figure. According to Huygen’s principle, every point on AB acts as a source of secondary wavelets. At first, wave incidents at point A and then to points C, D and E. They form a sphere of radii AA1, CC1 and DD1 as shown in figure.
A1E represents the tangential envelop of secondary wavelet in forward direction.
In ΔABE and ΔAA1E,
∠ABE = ∠AA1E = 90°
Side AE = Side AE
AA1 = BE = distance travelled by wave in same time
So, these triangles are congruent.
So, ∠BAE = i and ∠BEA =r
Thus, i = r
Hence, angle of incidence is equal to the angle of reflection. This is the first law of reflection.
Since, the incident wavefront AB, normal and reflected wavefront A1E lies in same plane, it verifies the second law of reflection.
In this way, laws of reflection is verified by Huygens’s principle.