Course description

4.1 Theory of light:

What is light and how the light energy is propagated through space (i.e., the nature of light) are discussed in Physical Optics.

(i) Corpuscular theory (Newton): A luminous body continuously emits invisible, tiny, light, and elastic particles called corpuscles. The different colors were due to different sizes of the corpuscles. Rectilinear propagation, Reflection, Refraction etc., ate satisfactorily explained (Fig. 1). But Interference, diffraction, polarization, photoelectric effect, etc. cannot be explained.

(ii) Wave theory (Huygens): Light propagates in a hypothetical ether medium in a shape of wave. Ether has a high elastic coefficient almost like a rigid body but density is very poor (Fig. 2). The different colors were due to the difference in the wavelengths. It can explain reflection, refraction, interference, diffraction.  But polarization, photoelectric effect, etc. cannot be explained.

(iii) Electromagnetic theory (Maxwell): Light and similar forms of radiation are made up of moving electric and magnetic forces and move as waves (Fig. 3). It does not need any medium. It can explain the polarization but cannot explain the photoelectric effect.

(iv) Quantum theory (Planck): Every atom acts like a oscillator and absorbs or emits energy in intermittent, and discontinuous amounts equal to integral multiple of a certain energy unit, hf, called quantum. It has Wave-Particle Duality character (Fig. 4). It can explain photoelectric effect but interference, diffraction, etc., cannot be explained.

                Fig. 1                                    Fig. 2                                    Fig. 3                                       Fig. 4

      Wave theory of light:   

(i)               From a source the light energy was supposed to be radiated in the form of spherical waves (Fig. 5).

(ii)             In the mode of propagation, the vibrating particles execute a periodic motion due to elasticity of the medium, gravity, and surface tension.

(iii)           The periodic motions of the particles of the medium produce a wave motion (Fig. 6).

(iv)            The disturbance (wave) produced by the vibrating particle will travel with equal velocity in every direction (Figs 5 and 7).

                    Fig. 5                                               Fig. 6                                                    Fig. 7

Wave front: The locus (set of points whose location is determined) of all the neighboring particles in the medium which are just being disturbed at that instant of time and are consequently in the same state of vibration. Figs 8 and 9 show the spherical and plane wave fronts.

                              Fig. 8                                                                     Fig. 9 

    Huygens’ principle:

(i)          Every point on a primary wavefront may be considered as a secondary source of disturbance (Fig. 10).

(ii)        Secondary wavelets spread out from each one of these secondary source into the medium with the same velocity as the original wave (Figs 10 and 11).

(iii)      The envelope of all the secondary wavelets after any given interval of time gives rise to the secondary wavefornt (Fig. 10).

                       

                                  Fig. 10                                                                      Fig. 11

    Principle of superposition: (Fig. 12)

(i)          When a medium is disturbed simultaneously by more than one wave, the instantaneous resultant displacement of the medium at every point at every instant is the algebraic sum of the displacement of the medium that would be produced at the point by the individual wave trains if each were present alone.

(ii)        After the superposition at the region of crossover, the wave trains emerge unhampered as if they have not met each other at all. Each wave train maintains its individual characteristics. Each waves train behaves as if others are absent.

            

                                                                                                                   Fig. 12

Suppose two trains cross each other at a certain point. Let y1 and y2 be the displacements of the point produced by the first and second wave in the absence of each other. Therefore, the resultant displacement y of the point due to the two waves acting together is expressed by  y = y1 ± y2.

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