YOUNG'S DOUBLE SLIT EXPERIMENT (Y.D.S.E.) In 1802 Thomas Young devised a method to produce a stationary interference pattern. This was based upon division of a single wavefront into two; these two wavefronts acted as if they emanated from two sources having a fixed phase relationship. Hence when they were allowed to interfere, stationary interference pattern was observed. Max Max Central Max Max Max 8 Young's Arrangement to produce stationary interference pattern by division of wave front S, into S, and S
Max Incident wave Max Max So Max Max Max Max
2 2 Path difference -SP-SP ||| y+-+D2-111 y 2 2 2 Approximation : For d, we can approximate rays r 1 and r 2as being approxi mately parallel, at angle to the principle axis.
Now, SP-SP=SA=s,s, sin ApproximationI further if is small, i. .y << D, sin -tan - path difference-: d sin S, A r, and hence, path difference- y for maxima (constructive interference), d.y y ,n=0, 1, 2, 3 Here n 0 corresponds to the central maxima n 1 correspond to the 1st maxima n +2 correspond to the 2nd maxima and so on.
for minima (destructive interference) 2 2 2 (2n -1) 2 2 (2n -1) n-1, 2,.3 2d consequently, y- n- 1, - 2, -3 2d Here n t 1 corresponds to first minima, n t2 corresponds to second minima and so on
Fringe width: It is the distance between two maxima of successive order on one side of the central maxima. This is also equal to distance between two successive minima. fringe width d B:-a 11 maxima II minima D --Y.-I maxima S minima D Notice that it is directly proportional to wavelength and inversely proportional to the distance between the two slits - _ Central maxima B fringe pattern in YDSE
COHERENCE: Two sources which vibrate with a fixed phase difference between them are said to be coherent. The phase differences between light coming form such sources does not depend on time. In a conventional light source, however, light comes from a large number of individual atoms, each atom emitting a pulse lasting for about 1 ns. Even if atoms were emitting under similar conditions, waves from different atoms would differ in their initial phases. Consequently light coming from two such sources have a fixed phase relationship for about 1ns, hence interference pattern will keep changing every billionth of a second. The eye can notice intensity changes which lasts at least one tenth of a second. Hence we will observe uniform intensity on the screen which is the sum of the two individual intensities. Such sources are said to be incoherent. Light beam coming from two such independent sources do not have any fixed phase relationship and they do not produce any stationary interference pattern. For such sources, resultant inten- sity at any point is given by II,I 2
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