Overview: Wave Nature of Light : Huygens' Principle

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'.

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.

\[t=\frac{D}{v}=\frac{D}{c/n}=\frac{nD}{c}\]

OR

d = n D.

λ_w = \[\frac {λ}{n}\]

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 :

1. 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'.
2. The secondary wavelets travel in the medium in all directions with the speed of the original wave (light) in the medium.
3. The envelope of the secondary wavelets in the forward
   direction at any instant gives the new wavefront at that instant.

• 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.

• 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.

• 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 sin⁡i/sin⁡r\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.