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Nature and Propagation of Light

 Nature and Propagation of Light 

Wave Theory of Light: The Subject of optics has been divided into two groups that are as  follows:  

i. Ray Optics 

ii. Wave Optics 

Ray Optics assumed that light consist of rays. A ray of light is the straight line path followed  by light going from one point to another. 

According to the wave theory of light, the light is the form of energy which transfer in a  medium in the form of transverse wave motion. 

Wave Front: 

According to wave theory of light, a source of light sends out disturbance in all direction in a  homogenous medium. The disturbance will reach in same phase to all the particles of the  medium located at the same distance from the source of light and hence at any instant, these  particle must be vibrating in phase with each other. The Locus of all such particle of the  medium vibrating in the same phase is called the wave front. Depending upon the shape of  source of light, wave front can be of 3 types. 

1. Spherical Wave Front: A spherical wave front is produced by a point source of light as a  locus of all such point which are equidistance from the point source will be a sphere.

2. Cylindrical Wave Front: When the source of light is linear in shape such as a slit (tube  light), The cylindrical wave front is produced. All the point equidistance from a linear  source lies on the cylinder. 

3. Planer Wave Front: A small part of spherical or a cylindrical wave front due to a distance  source will appear plane and hence is called plane wave front. It will be represented by  a straight line. 

  

OR 

Huygens’s Principle: 

Huygens gave a hypothesis for geometrical construction of the position of a common wave  front at any instant during the propagation of wave. The principle is based on the following  assumption: 

i. Each point on the Primary Wave front act as a source of secondary wavelets, sending  out disturbance in all direction in a similar manner as the original source of light  does. 

ii. The new position of the wave front at any instant is given by the forward envelop of  the secondary wavelets at that instant.

Consider a point source of light S. Let AB is a section of spherical wave front at any time t. In  order to find the new position of wave front, at time t+ Δt , Consider a number of points a, b, c,  d,………. Which are taken of the primary wave front. These points acts as the source of  secondary wavelets. In time Δt, light will travel a distance C. Δt . Taking point a, b, c….. as the  center, spheres each of radius C. Δt are drawn. The forward envelop of A’B’ of these Spheres  are gives the position of wave front at time t+ Δt and is called secondary wave front.  

The same procedure is to be adapted for finding the new position of a cylindrical or a planer  wave front.

Reflection on the Basis of Wave Theory 

Let XY be the reflecting surface and AP is a place wave front just incident on it. The line LA and  MP which are perpendicular to the incident wave front, represent the incident rays. If AN is a  normal to reflecting surface at A then  

∠LAN = ∠i = Angle of incidence.  

The Wave front arrives at point A first of all and will arrive at point B, C, ………… later in time.  Thus different point on the reflecting surface will become the source of secondary wavelets at  different instant of time. When the disturbance from point P reached point P’ on the surface,  the secondary wavelets from A on the surface will have acquired radius AA’, BB’, CC’ ………  respectively. The reflected wave front will be the tangent plane A’P’ touching all the secondary  wavelets. If P’N’ is normal to the reflecting surface at P’ then 

∠N’P’M’ = ∠r = angle of refraction.  

As the velocity of light does not change on reflection and the distance PP’ and AA’ are traveled  in the same time  

∴ AA’ = PP’ 

Now In Right angled Triangle APP’ and AA’P’, 

∠AA’P = ∠APP’ (Right angle of both triangle) (R) 

AP’ = AP’ (common side) (H) 

AA’ = PP’ (already Proved) (S) 

Therefore, Triangles APP’ and AA’P’ are congruent by RHS axiom.  

Hence, ∠PAP’ = A’P’A  

As the angle between two lines is same as the angle between their perpendiculars so that,  ∠PAP’ = ∠i  

 ∠A’P’A = ∠r  

Hence, ∠i = ∠r. The law of Reflection are verified on the basis of wave theory.  

∙ What is the difference between wave front and wavelets?  

Wave front at any instant is defined as the locus of the particles of the medium vibrating  in the same phase. Every point on the wave front acts a source of disturbance, these  points are called wavelets.
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