Question

Prove laws of reflection using Huygens’ principle.

Answer 1

Laws of reflection

1. Let us consider a parallel beam of light, incident on a reflecting plane surface such as a plane mirror XY.
2. The incident wavefront is A’B’ and the reflected wavefront is AB in the same medium.
3. These wavefronts are perpendicular to the incident rays L, M and reflected rays L ‘, M’ respectively.
4. By the time point A of the incident wavefront touches the reflecting surface, point B is yet to travel a distance BB’ to touch the reflecting surface B’.
5. When point B falls on the reflecting surface at B’, point A would have reached A’. This is applicable to all the points on the wavefront.
6. Thus, the reflected wavefront A’B’ emanates as a plane wavefront. The two normals N and N’ are considered at the points where the rays L and M fall on the reflecting surface. As reflection happens in the same medium, the speed of light is the same before and after the reflection.
7. Hence, the time taken for the ray to travel from B to B’ is the same as the time taken for the ray to travel from A to A’. Thus, the distance BB’ is equal to the distance AA’ (AA’ = BB’)
   
   1. The incident rays, the reflected rays the normal are in the same plane.
   2. Angle of incidence,
      ∠ i = ∠ NAL = 90° – ∠ NAB = ∠ BAB’
      Angle of reflection,
      ∠ r =∠ N’B’M’ = 90° – ∠ N’B’A’=∠ A’B’A
8. For the two right-angle triangles, ∆ ABB’ and ∆ B’A’A, the two triangles are congruent. As per the property of congruency; the two angles, ∠ BAB’ and ∠ A’B’A must also be equal.
   i = r
   hence the laws of reflection is proved.