Question
What are the different types of wavefronts, and how do we construct each using Huygens’ principle?
Solution — Step by Step
A wavefront is the locus of all points in a medium that are in the same phase of oscillation. Think of it as a surface connecting all “crests” (or all “troughs”) at any instant.
The direction of wave propagation is always perpendicular to the wavefront — these are called rays.
| Type | Source | Shape | Ray Direction |
|---|---|---|---|
| Spherical | Point source | Expanding spheres | Radially outward |
| Cylindrical | Line source (like a slit) | Expanding cylinders | Perpendicular to the cylinder axis |
| Plane | Very distant source (or after lens) | Flat planes | All rays parallel |
graph TD
A[What is the source?] --> B{Source type?}
B -->|Point source, nearby| C[Spherical Wavefront]
C --> C1[Expanding sphere, diverging rays]
B -->|Line source or slit| D[Cylindrical Wavefront]
D --> D1[Expanding cylinder]
B -->|Point source very far away| E[Plane Wavefront]
E --> E1[Flat surface, parallel rays]
F[Key Rule] --> G[At large distances, any wavefront becomes approximately plane]
G --> H[Because sphere of large radius looks flat locally]According to Huygens’ principle, every point on the current wavefront acts as a secondary source. The new wavefront is the envelope of all secondary wavelets.
Spherical wavefront: Each point on the sphere emits a spherical wavelet. The forward envelope is a larger sphere — the wavefront expands outward.
Plane wavefront: Each point on the flat surface emits a spherical wavelet. All wavelets travel the same distance in the same time, so the forward envelope is again a flat plane — the wavefront moves forward as a flat sheet.
Cylindrical wavefront: Points on the cylinder emit wavelets that collectively form a larger cylinder.
The beauty of Huygens’ construction: it naturally explains how wavefronts propagate, reflect, refract, and diffract.
Why This Works
Wavefronts are a powerful way to visualise wave propagation. Instead of tracking individual oscillations, we track surfaces of equal phase. The geometry of the source determines the wavefront shape, and distance transforms curved wavefronts into flat ones (just as the curved Earth appears flat locally).
For CBSE boards, draw neat diagrams showing the source, wavefronts as concentric circles (spherical) or straight lines (plane), and rays perpendicular to them. Label everything. The diagram carries significant marks in the 3-5 mark questions on wave optics.
Alternative Method
We can also define wavefronts mathematically. For a point source at origin, the wavefront at time is the sphere . For a plane wave moving in the -direction, the wavefront is the surface (a vertical plane perpendicular to ).
Common Mistake
Students draw rays parallel to wavefronts instead of perpendicular. Rays ALWAYS hit the wavefront at 90 degrees. For a spherical wavefront, rays point radially outward. For a plane wavefront, all rays are parallel. Drawing rays along the wavefront is a fundamental error that reveals a misunderstanding of the wave-ray relationship.