Wave Optics

Concept:
Huygens’ principle explains wave propagation using secondary wavelets. The new wavefront at any time is the envelope (tangent surface) of these secondary wavelets. This principle helps derive reflection and refraction laws geometrically.
Step 1: Statement of Huygens’ Principle
Every point on a wavefront behaves like a source of secondary spherical wavelets. The forward envelope of these wavelets gives the new wavefront.
Step 2: Reflection using Huygens’ Principle
Consider a plane wavefront incident on a plane mirror at an angle .
- Let AB be the incident wavefront.
- Point A touches the mirror first.
- After time , point B reaches the mirror.
During this time, a secondary wavelet from A spreads as a circle (in 2D).
Step 3: Construct reflected wavefront
Draw a tangent from point B to the secondary wavelet from A.
This tangent gives the reflected wavefront.
From geometry of construction: Thus, angle of incidence equals angle of reflection. (OR) Refraction using Huygens’ Principle
Step 4: Refraction setup
Let a wavefront travel from medium 1 to medium 2 with speeds and .
- Point A enters second medium first
- Point B still in first medium
Wavelets from A travel slower or faster depending on medium.
Step 5: Construct refracted wavefront
After time :
- Distance traveled by A =
- Distance traveled by B =
Using right triangle geometry: Using refractive index relation: We get: This is Snell’s law of refraction.