## WAVE NATURE OF LIGHT

## Huygens’ Wave Theory

(i) Each point on a wave front acts as a source of new disturbance and emits its own set of spherical waves called secondary wavelets. The secondary wavelets travel in all directions with the velocity of light so long as they move in the same medium.

(ii) The envelope or the locus of these wavelets in the forward direction gives the position of new wavefront at any subsequent time.

A surface on which the wave disturbance is in the same phase at all points is called a wave front.Wave optics involves effects that depend on the wave nature of light. In fact, it is the results of interference and diffraction that prove that light behaves as a wave rather than a stream of particles (as Newton believed).

Like other waves, light waves are also associated with a disturbance, which one consists of oscillating electric and magnetic field. The electric field associated with a plane wave propagating along the x-direction can be expressed in the form:

E

^{→}= E^{→}_{o}[sin ( λt - kx + θ_{o}) ]Where λ, k and θ

_{o}bearing their usual meanings.

Points to remember regarding Interference

_{1}and A

_{2}superimpose at a point, the amplitude of resultant wave is given by

A = √A

_{1}

^{2}+ A

_{2}

^{2 }+ 2A1A2 cosΦ

Where θ is the phase difference between the two waves at that point.

_{o}C E

_{o}

^{2}. C = speed of light, E

_{0}= electric field amplitude

_{1}+ I

_{2}+ 2√I

_{1}I

_{2}cosθ.

Hence for I to be constant, must be constant.

_{1}+ I

_{2}.

**Coherent sources have a constant phase relationship i.e. one that does not change with time.**

**Determination of Phase Difference:**

The phase difference between two waves at a point will depend upon

(a) The difference in path lengths of the two waves from their respective sources.

(b) The refractive index of the medium

(c) Initial phase difference, between the sources, if any.

(d) Reflections, if any, in the path followed by waves.

= [ Optical path difference / λ ] x 2π = [ µ(Geometrical path difference) / λ ] 2π

Where λ is the wavelength in free space.