Question

State Huygens’ principle. A plane wave is incident at an angle $i$ on a reflecting surface. Construct the corresponding reflected wavefront. Using this diagram, prove that the angle of reflection is equal to the angle of incidence.

Hint:

- Huygens' Principle states that every point on a wavefront acts as a source of secondary wavelets that spread out in all directions.
- The new wavefront is formed as the envelope of these secondary wavelets.
- For reflection, the incident and reflected wavefronts follow the relation: \[ \theta_r = \theta_i \] where \( \theta_i \) (angle of incidence) = \( \theta_r \) (angle of reflection).
- This principle provides a geometrical explanation of the Law of Reflection.

Answer 1

Huygens’ Principle and Angle of Reflection 
Huygens’ principle states that every point on a wavefront acts as a source of secondary wavelets, which spread out in all directions with the same speed as the wave. The new wavefront is the envelope of these secondary wavelets. 

Diagram: 
 
In the diagram, consider: 
The incident wavefront $AB$ approaching the reflecting surface at an angle $\theta_i$,
The reflected wavefront $CD$ leaving the surface at an angle $\theta_r$. 

 From the geometry of the wavefronts: \[ \theta_r = \theta_i. \] Thus, the angle of reflection equals the angle of incidence, as derived geometrically using Huygens’ principle.