Definitions [2]
Definition: Wavefront
If we draw a surface in a medium such that all the medium particles lying in the surface are in the same phase of oscillation, then the surface is called a 'wavefront'.
Definition: Optical Path
The optical path travelled by a light ray is the product of the refractive index of the medium and the actual distance travelled by light in that medium.
Formulae [2]
Formula: Variation of Wavelength in Media
λw = \[\frac {λ}{n}\]
Formula: Optical Path
\[t=\frac{D}{v}=\frac{D}{c/n}=\frac{nD}{c}\]
OR
d = n D.
Theorems and Laws [1]
Principle: Huygens' Wave Theory
Huygens proposed a geometrical construction to explain the propagation of a wavefront in the medium and determined the position of the wavefront after any interval of time. This is known as 'Huygens' principle' and may be stated as follows :
- Every particle of the medium situated on the wavefront acts as a new wave-source from which fresh waves originate. These waves are called ‘secondary wavelets'.
- The secondary wavelets travel in the medium in all directions with the speed of the original wave (light) in the medium.
- The envelope of the secondary wavelets in the forward
direction at any instant gives the new wavefront at that instant.
Key Points
Key Points: Reflection of a Plane Wave at a Plane Surface
- According to Huygens’ principle, each point on the incident plane wavefront acts as a source of secondary wavelets, whose forward envelope gives the reflected wavefront.
- The reflected wavefront is obtained by drawing a common tangent to the secondary wavelets, showing that reflection follows wavefront construction.
- Using this construction, the laws of reflection are obtained:
angle of incidence equals angle of reflection (i = r), and
incident ray, reflected ray, and normal lie in the same plane.
Key Points: Plane Wavefront: Reflection and Refraction
| Incident Wavefront | Medium | Nature of Wavefront after Reflection / Refraction |
|---|---|---|
| Plane | Plane reflecting surface | Plane |
| Plane | Plane refracting surface | Plane |
| Plane | Prism | Plane |
| Plane | Convex lens | Spherical (converging) |
| Plane | Concave lens | Spherical (diverging) |
| Plane | Concave mirror | Spherical (converging) |
Key Points: Refraction of a Plane Wave at a Plane Surface
- Refraction of a plane wavefront can be explained using Huygens’ principle by constructing secondary wavelets in the second medium.
- The refracted wavefront is the forward envelope of secondary wavelets formed in the second medium.
- Rays are normal to wavefronts, so the angles between wavefronts give the angles of incidence and refraction.
- Huygens’ construction leads to Snell’s law, showing that sini/sinr\sin i / \sin rsini/sinr is constant for two given media.
- Wave theory proves that light travels slower in optically denser media, a result confirmed by Foucault’s experiment.
Key Points: Wavefront
- In a homogeneous isotropic medium, wavefronts are always perpendicular to the direction of wave propagation.
- Rays are drawn normal to the wavefront and indicate the direction of propagation of the wave.
- A point source produces spherical wavefronts, with rays spreading radially outward.
- A plane wavefront consists of parallel rays, while a linear source produces cylindrical wavefronts.
