Study the interference of light using Helium - Neon Diode Laser.

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TO STUDY THE INTERFERENCE OF LIGHT BY USING HELIUM -DIODE LASER 
COHERENT SOURCES

As we see later, light waves from a sodium lamp, for example, are due to energy changes in the sodium atoms.  The emitted waves occur in bursts lasting about second. The light waves produced by the different atoms are out of phase with each other, as they are omitted randomly and rapidly.  We  call such sources of light waves as these atoms incoherent sources on account of the continual change of phase.

Two sodium lamps X and Y both emit light waves of the same colour or wavelength. But owing to the random emission of light waves from their atoms, their resultant light waves are constantly out of phase.  So X and Y are incoherent sources.  Coherent sources are those which emit light waves of the same wavelength or frequency which are always in phase with each other or have a constant phase difference. As we now show, two coherent sources can together produce the phenomenon of interference.

INTERFERENCE OF LIGHT WAVES, CONSTRUCTIVE INTERFERENCE

Suppose two sources of  light, A, B have exactly the same wavelength and amplitude of vibration, and that their vibration are always in phase with each other, fig.1. The two sources A and B are therefore coherent sources.

 

                                          fig.1

Their combined effect at a point is obtained by adding algebraically the displacements at the point due to the sources individually.  This is known as the principle of superposition.  So, their resultant effect at X, for example, is the algebraic sum of the vibrations at X due to the source A alone and the vibrations at X due to the source B alone.  If X is equidistant from A and B, the vibrations at x are to the two sources are always in phase as (i) the distance AX traveled by the wave starting from A is equal to the distance BX traveled by the wave starting from B; (ii) the sources A and B are assumed to have the same wavelength and to be always in phase with each other.

                                iii) resultant

fig. 2

Figure 2(i) and (ii) illustrate the vibrations at X due to A and B, which have the same amplitude.  The resultant vibration at X is obtained by adding the two curves, and has an amplitude double that of either curve, Figure 2 (iii). Now the energy of a vibrating source is proportional to the square of its amplitude .  Consequently the light energy at X is four times that due to A or B alone. A bright band of  light is thus obtained at X.  As A and B are coherent sources, the bright band is permanent.  With wave crests and troughs arriving at X at the same time, we say that the bright band is due to constructive interference of the light waves from A and B at  X.

If Q is a point such that BQ is greater than AQ by a whole number of wavelengths ( Figure 1), the vibration at Q due to A is in phase with the vibration there due to B.  A permanent bright band is then obtained at O.

Generally, a permanent bright band is obtained at any point Y if the path difference, BY – AY, is given by

                        BY – AY =

Where     is the wavelength of the sources, A, B and n = 0, 1 2 and so on

We now see that permanent interference between two sources of  light can only take place if they are coherent sources, that is they must have the same wavelength and be always in phase with each other or have a constant phase difference.  Thus, implies that the two sources of light must have the same colour. As we see later, two coherent sources of  light can be produced by using a single primary source of  light.

DESTRUCTIVE INTERFERENCE

Consider now a point P in Figure 19.1 whose distance from B is half a wavelength longer than its distance from A, AP – BP =     .  The vibration at P due to B will then be 180   out of  phase with the vibration these due to A, Figure 19.3 (i), (ii).  The resultant effect at P is thus zero, as the displacements at any instant are equal and opposite to each other, Figure 19.3(iii). No light is therefore seen at P.  With a wave crest from A

Arriving at a P at the same time as a wave trough from B, the permanent dark band here is said to be due to destructive interference of the waves from A and B.

SEPARATION OF  FIGURES

We can find the separation x of the fringes in terms of d, the separation of the slits S , S  the distance d of the screen t from the slits and the wavelength     of the monochromatic light coming from the slits Figure 19.7(i).

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The center of the fringes is at O, where the perpendicular bisector MO of  S1 S2 meets T.  Here the path difference S2O – S1O = O, since the paths are equal. On either side of O, the fringes cover only a very small distance as the wavelength of light is very small. So if P is the nth bright fringe from O, with S1 S2very small (0.4 mm, for example) and D very large relatively (1.0 m, for shown.  The line MR to P  is also parallel to S1A and  S2B.

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