Question

Derive laws of reflection of light using Huygens’ principle.

Hint:

Huygens’ principle helps us understand how waves propagate and reflects, explaining the equal angles of incidence and reflection.

Answer 1

Step 1: Huygens' Principle.
According to Huygens' principle, every point on a wavefront acts as a source of secondary wavelets that spread out in all directions. The new wavefront is the surface tangent to all the secondary wavelets.
Step 2: Reflection of Light.
Consider a wavefront of light incident on a reflecting surface. Let \( A \) be the point on the wavefront that hits the surface at an angle \( \theta \). At the point of incidence, secondary wavelets are generated, and the reflected wavefront is formed by the tangent to these wavelets.
Step 3: Geometry of Reflection.
By applying the principle of reflection at the point of incidence, the angle of incidence \( \theta_i \) is equal to the angle of reflection \( \theta_r \): \[ \theta_i = \theta_r \]
Step 4: Laws of Reflection.

- The incident ray, the reflected ray, and the normal to the surface all lie in the same plane.
- The angle of incidence is equal to the angle of reflection.
Step 5: Conclusion.
Huygens' principle explains the laws of reflection by showing that each point on the incident wavefront acts as a secondary source, leading to the reflection of light with the same angle of incidence and reflection.