Interference of Waves

                                                            Two beam Interference
Two rods attached to a bar Is allowed to vibrate in and out of water at constant frequency each rod will generate a soot of its own set of ripples. The principle of superposition states that when the crest and the through of one ripple system. The resultant amplitude of the system (in dis case water) will be equal to sum of individual amplitude.

The sum of the individual amplitude can create either constructive or a destructive interference. Constructive or a destructive interference. Constructive interference occurs because the ripples of one system is in phase with the other system. Also when the ripples of two systems are in phase, it is constructive conversely a destructive occurs when two ripples of a system are not in phase. It also means when the crest of one phase meets with the through of the other. When one or two system produces waves, it is the ripples that travel outward the nodes at end the antinodes stays in their fixed point just as stationary waves. Condition for obtaining stationery and interference pattern:

 The frequency of the wave must be constant

 These must be constant phase difference between the waves leaving the source.

Coherence sources: - An example is a sodium lamp Light waves from Sodium lamp is due to energy changes in sodium atom. The emitted wave occurs in burst lasting for about losses, light waves emitted by different atoms are out of phase and are said to be incoherent. When we place two Na waves i.e. Waves from two different Na lamps. If the two waves are out of phase there would be incoherent (A destructive one)

CONDITION FOR INTERFERENCE

Let us examine the fig above with the same amplitude of vibration and are in phase with each other. The combined effect i.e the resultant is due to the amplitude. The resultant of the effect is being defined by the principle of superposition.

       N/B
(1) The x is equidistant from A and B(the vibration x due to A and B are always in phase)
(2) The resultant at x is due to the algebraic addition of vibrations of A and B
(3) A and B are assumed to have the same wavelength.

Resultant at x is said to be constructive. The conditions above are satisfied, means the two sources of light A and B Which means we can now observe bright band point of light at x due to constructive interference? Consequently if Q is a point such that BQ is grater than AQ by the wavelength then the vibration at Q due to A is in phase due to vibration at B and permanent bright band is observed at Q.

 

 Permanent Dark Light would be seen at P

Summary:- If the path length difference of the two waves is zero or a whole number of the path length, a permanent dark light would be seen and conversely if the path length or difference in path length is odd number, a permanent dark light would be seen. Young’s two Slit Experiment, Young in 1801 demonstrated an experiment on interference between two monochromatic light.

Conditions for Interference

 Two coherent sources of light must be produced
 The two sources of light must be close to each other.

Young placed a monochromatic light in front of a narrow slit S and arranged two additional very narrow A and B close to each other. Young then observed he explained this by considering A and B , since the light diverging from A have the some frequently and always in phase with the one diverging from B. A and B are said to be two closed coherent source of light. Interference the takes place when the beam over lap with each other. Then OA =OB, therefore a bright bond of light.