Wave theory

involves huygen's principle,laws of reflection and refraction

1. Unit 1 Wave theory

2. Light energy originates somewhere within an atom and ends its existence ,when it enters another atom or a molecule . Light is transferred from the source of light to the eye,either by 1. the motion of material particles 2. means of wave disturbance travelling through the medium All the theories based on the experimental facts such as , 1.Light propagates through vaccum with a velocity c. 2. Light travels in a straight line in a homogeneous medium. 3.Light is refelected from a smooth surface.(Reflection) 4.Light is refracted when it travels from one medium into another(Refraction). 5. Light gets dispersed into different colours , on passing through a triangular prism (Dispersion). 6. Light shows interference, diffraction and polarization. 7. When light of suitable frequency falls on certain metals, electrons are ejected from them (Photoelectric effect).

3. The important theories of light are : 1. Newton's corpuscular theory 2. Huygen's wave theory 3. Maxwell's electromagnetic theory 4. Planck's quantum theory Newton's corpuscular theory fails to explain the phenomena of interference, diffraction and polarization.

4. Huygen’s Wave theory

5. Christian Huygen proposed the wave theory of light. According to this theory, light propagates from the source in the form a wave. Each point in a source of light sends out waves in all directions in hypothetical medium called ether. Ether was assumed to be continuous medium which pervades all space. Due to tremendous velocity of light, it was assumed that ether has very large elasticity and extremely low density. The existence of ether had to be assumed because for the propagation of a wave motion, a medium is necessary. Huygens assumed that light waves are longitudinal. Using wave theory, Huygens could explain reflection, refraction, simultaneous reflection and refraction, total internal reflection, dispersion, double refraction etc. However, it fails to explain the rectilinear propagation of light, diffraction and polarization. However , Huygen's wave theory could not prove the presence of ether.

6. Thomas Young analyzed and explained the colours seen in thin films like soap bubbles which was based on the concept of superposition of waves. Fresnel framed a mathematical analysis of wave theory which removed the defects of Huygen ' s principle but also it explained the concept of diffraction of light and rectilinear propagation of light at macroscopic level. A series of experiments on diffraction of light conducted on development of electromagnetic waves by Maxwell in 1860 which correctly predicted the speed of light. The electromagnetic theory was highly successful in explaining the propagation of light waves .

7. Wavefront and different types A source of light sends out disturbance in all directions . In a homogeneous medium, the velocity of light is the same in all directions. Therefore , all the particles of the medium at the same distance from the source of light vibrate in the same phase . The locus of all such particles vibrate in the same phase is called the wavefront . A wavefront is defined as a cross sectional surface of constant phase in a light beam . A wavefront is a surface or line in the path of a wave motion the disturbances at every point have the same phase.

8. Types of Wavefront : Depending on the nature of the source of light there are 3 types of wavefronts : Spherical wavefront Cylindrical wavefront Plane wavefront . Spherical Wave front : A point source kept in a isotropic medium Emits spherical wavelength with the source As the centre of the wavefront,because All points are equidistant from the source lie on the surface

9. Cylindrical Wavefront : When the source of light is linear (slit) all the points equidistant from the linear source of a cylinder .such wavefront known as cylindrical wavefront . Plane wavefront : At a large distance from a source of any kind ,the wavefront will appear plane .this is called plane wavefront . For plane wavelength ,the rays are parallel ,for spherical wavefronts the rays are converging or diverging , Parallel rays indicate plane wavefront . Diverging rays indicate diverging spherical wavefront . Converging rays indicate converging spherical wavefront .

10. Huygen’s Principle Every point on wavefront is considered to be centre of disturbances and sends out secondary wavelets in all directions with the velocity of light in the medium. The envelope or the locus of these wavelets in the forward direction gives the position of the new wavefront at any subsequent time.

11. Laws of Reflection and Refraction: 1. Laws of Reflection ( i ) The angle of incidence is equal to the angle of reflection. ( ii) The incident wavefront . the reflected wavefront and normal to the reflecting surface all lie in the same plane . 2 .LAWS of Refraction ( i ) The incident wavefront , the refracted wavefront and the normal to the refracting surface. all lice the same plane. ( ii) The ratio of image distance to the object distance is a constant quantity.

12. Huygen's Principle Applied to Reflection let be a point source of light situated at a distance OP from the plane reflecting surface XY . Let APB be the section of the incident spherical wavefront touching the plane reflecting surface XY at P at any instant. By the time the disturbance at A reaches the surface C and that at B reaches D the secondary wave from P must have travelled a distance PM equal to AC or BD.

13. The centre of curvature of the reflected wavefront CMD is I which is the image of O. Also the curvature of the reflected wavefront is the same as that of the incident wavefront . Since CLD and CMD form the arcs of a circle we have CP 2 = 2PL•OL or OL = CP 2 /2PL and CP 2 =2MP• MI = 2MP But PL = MP, MI = OL Thus, a spherical wavefront APB, on reflection from a plane mirror, is sent back as a spherical wavefront CMD which appears to have diverged from a point I. such that IM=OL or 1P+MP= OP + PL or IP=OP u=v i.e Object distance= image distance

14. Refraction of a spherical spherical wave at a plane surface wavefront at a plane surface Let XPY be a plane surface separating two media. Let the refractive indices of the two media be n, and et, and vi and , be the velocities of light in them respectively. Let 0 be a point source of light situated at a distance u from the plane surface XY. Let APB be the spherical wavefront be incident from the rarer medium of absolute refractive index n, at P . Let the time taken by the disturbance at A to reach the surface at C or that at B to reach D be t seconds. Then AC = BD = v 1 t ……....( 1) If there were no medium 2. then the disturbance at P would have reached the point N in a time t. Then PN=v 1 t……….(2)

15. The disturbances at P reaches the point M in the 2 nd medium such that PM = v 2 t ………..(3) Dividing (3) by (2) = = = …..(4) Let the image distance =(PI) be v For the spherical surface CND, CP 2 =2PN.ON PN= = = = (ON=OP) ….(5) Similarly ,for the spherical surface CMD, CP 2 =2PM.IM PM= = = …………(6) Dividing (6) and (5) = = = ……..(7) Where 2 = refractive index of the second medium wrt first medium. = =