PHYSICS11 4.Laws Of Motion

  Wave theory of Light

                Introduction

                   Light is the form of energy which makes object visible to our eyes. Light has dual nature particle as well wave nature. There were two theories proposed to discuss nature of light. 

   (1) Newton’s corpuscular theory of light, based on the particle nature of light 

 (i) Every source of light emits large number of tiny particles known as 'corpuscles' in a medium surrounding the source. 

(ii) These corpuscles are perfectly elastic, rigid and weightless. 

(iii) The corpuscles travel in a straight line with very high speeds, which are different in different media. 

(iv)  One gets a sensation of light when the corpuscles fall on the retina. 

(v) Different colours of light were due to different sizes of corpuscles. 

This theory could explain reflection, refraction and inverse square law but had drawbacks as follows: 

(I) It could not explain partial reflection and refraction at the surface of a transparent medium. 

(2) It was unable to explain phenomenon such as interference, diffraction, polarization etc. 

This theory was proposed by Planck to explain black body radiation. According to this theory light is propagated in the form of packets of light energy there is no change in the mass of the source of light. called quanta. Each quantum of light called photon has energy E = hv, where v is the frequency of light and 'h' is Planck's constant. 

(3) This theory predicted that speed of light in a denser medium is more than the speed of light in a rarer medium which was experimentally proved wrong by Foucault. Hence the Newton's corpuscular theory was rejected. 

(4) When particles are emitted from the source of light then mass of the source of light must decrease but experiments showed that 

Huygens wave theory of light

                 Que.1: explain in brief Huygens wave theory of light

OR

Explain Merits & Demerits of Huygens wave theory of light 

Ans: This theory was proposed in 1678 by a Dutch physicist Huygens. The main feature or characteristics of Huygens wave theory are,

 (1) Light travels from one place to another in vacuum or transparent medium in the form of waves.                

(2) These waves are emitted by the source of light & travel with uniform velocity in the homogeneous medium.

(3) When these waves are enters in our eyes we get   sensation of light.

 (4) Different colures of light are due to different wavelengths of lightwaves.                                                                                            

(5)To explain propagation of light waves through vacuum he suggested the existence of hypothetical medium called Luminiferous ether present everywhere.

 (6)  Experimentally he proved that velocity of light in rarer medium is greater than in denser medium.   

Merits of wave theory of light :-  

1)This theory satisfactory explains the reflection& refraction of light.

2) According to this theory the velocity of light in the rarer medium is greater than velocity of light in a denser medium& it is experimentally verified by him.

Drawbacks or demerits of the wave theory of light:-

1) According to this theory there is existence of Luminiferous ether medium in the universe. But experimentally it was found that there is no existence of such medium in the universe. 

2) Huygens did not mention anything about the nature of waves i.e. longitudinal or transverse.

3) This theory failed to explain the rectilinear propagation of light.

4) This theory failed to explain some phenomenon’s based on the particle nature such as photoelectric effect. Raman effect & Compton effect.                                                                                                                 

 Angstrom unit :- The  wavelength of light is very small so that bending of light is very small  round the obstacle in their path. it is expressed in the unit called as Angstrom unit represented by symbols AO  A.U. which is given as  1A.U.=10-8cm=10-10 m    

Que.2 Explain the concept of wave front?

Ans:-Concept of wave front- Consider a point source S of light in the air. The waves of light emitted by the source travel in all possible directions If c is the velocity of light in air, in time t each wave will cover a distance ct will reach the surface of sphere of radius ct with the surface as its centre.

Such a spherical surface is called as spherical wave front. All the point on this front is in same phase.

Definition of wave front: -

It is defined as the locus of all the points of the medium to which the waves reaching simultaneously, so that all the points are in the same phase.

  As time passes the wave front goes on expanding so that at a large distance from the point source, the spherical wave front is so large that its small part can be considered as the plane wave front. 

  There are three types of wave front.

 (a) Spherical wave front

(b)Plane wave front

 (c) Cylindrical wave front  

(a) Spherical wave front: - The wave front is originated from a point source of light.

(b)Plane wave front: - At longer distance from the point source the spherical wave front is so large that its small part can be considered as the plane wave front.                                                                                 (c) Cylindrical wave front:- a wave front original from liner sours like slit which give rise to cylindrical wave front.

Que.3 Define (i) wave front,

(ii) wave normal.

Ans:- (i)Wave front:-
- It is defined as the locus of all the points of the medium to which the waves reaching simultaneously, so that all the points are in the same phase.

(ii) Wave normal:- A perpendicular drawn to the surface of a wave front at any point in the direction of propagation of light is called wave normal.

 Que.4 : State Huygen’s  principle and explain Huygen’s construction of a spherical wavefront.

Ans: Huygens Principle:  

i) Each and every point on the wave front acts as a secondary source of light, sending out secondary waves in forward direction.

ii) Then the envelope of all these secondary waves at any later instant gives the new wave front at that instant.

Huygens construction of spherical wave front:-

1. Consider a point source S of light, situated in the homogeneous medium such as air.

2.  If A, B& C are the point situated from the same distance from the source. The waves emitted by the source reaches these points simultaneously, so that all the points will be on the spherical wave front.(i.e. XY be the spherical wave front) 

3. According to Huygens principle, as soon as the spherical wave front is formed, every point on its surface will acts as secondary source of light sending out secondary waves. 

4. To determine the new wave front after the time t, lets draw sphere with every point on the surface A,B &C as centre & radius ct. the tangent (x’Y’)to all these spheres will represent the new wave front after the time t as A’, B’ & C’ 

                                                                             

Que.5: Explain Huygen’s construction of a Plane wavefront.

Ans: Huygens construction for plane wave front: 

1. Suppose that XY is the part of plane wave front at any instant originated from point source of light placed at a very large distance. Suppose this wave front is travelling from left to right.

2.  Let A, B, C and D are the points on plane wave front XY.

3.  According to the Huygens’s principle these points acts as secondary source of light sending secondary waves in forward direction with velocity c. 

4. At any later instant `t’ each secondary wave covers a distance equal to ct. 

5. To determine the position of new wave front after time t, draw spherical wave fronts with radius ct and A, B, C and D as centre which cuts the rays at points A’, B’, C’, and D’ respectively.

6.  Draw a tangential surface X’Y’ touching to all spherical wave fronts at points A’, B’, C’ and D’. This surface X’Y’ represents the new wave front after time t. This new wave front is also plan wave front. 

 Que.6: Explain the reflection of light on the basis of wave theory of light with suitable ray diagram. 

OR

Prove the laws of reflections on the basis of wave theory of light with suitable ray diagram.

Ans:-Reflection of plane wave front from plane reflecting surface :    

1. Consider a plane wave front AB bounded by the two parallel rays PA & QB is obliquely incident on plane reflecting surface XY, such as plane mirror.

2.  As soon as the wave front reaches the point A, it will become the secondary source of light, sending out secondary waves. In the same medium. After the time t secondary waves from A reaches the point D, such that the distance AD=ct 

3. At the same time secondary waves from B reaches to the point C such that the distance BC=ct. 

4. In order to find the new wave front after the time t semi circle of radius AD. 

5. Draw a tangent CD to this semi circle. Hence, the point C&D are in the same phase, CD will represent new reflected plane wave front. 

6. From the geometry of fig.

XY=Reflecting surface  

      AB=plane incident wave front   

      DC=Reflected wave front               

      AM=Normal drawn  

   <APM=i=Angle of incidence  

  <DAM=r=Angle of reflection.

  

Thus the angle of incidence is equal to angle of reflection. The laws of reflections are proved.  

(1) The angle of incidence is equal to angle of reflection 

(2) The incident rays & reflected rays are lie opposite side of normal.

(3) The normal, incident rays & reflected rays are lie in the same plane.                                                                                                                                                                                    

Que.7: With the help of suitable diagram explain the refraction of light on basis of wave theory .

OR

On the basis of Huygens’s wave theory of light prove that the velocity of light in rarer medium is greater than velocity of light in denser medium.

Ans: - Refractions of light on the basis of wave theory:

1. Suppose that XY be a plane refracting surface separating a rarer & denser medium. Consider a plane wave front AB bounded by the two parallel rays PA & QB is obliquely incident on plane refracting surface XY,

2.  As soon as the wave front reaches the point A, it will become the secondary source of light, sending out secondary waves. In the denser medium.

       

1. After the time t secondary waves from A reaches the point D, such that the distance AD = c1t. At the same time secondary waves from B reaches to the point C such that the distance BC = c2t. The secondary wave from C gets refracted in the denser medium along CR, in the same time t.

2. Let c1  & c2 are the velocity of light in rarer & denser medium respectively. 

3. In order to find new refracted wave front after a time t draw a semi sphere of radius AD in the denser medium such that

4. AD = c1t 

5. Draw a tangent CD to the semi sphere since the point C & D are in the same phase ,Which represent new refracted wave front in the denser medium.