Rationalised 2023-24
263
Wave Optics
Since the distances S1 P and S2 P are equal, waves from S1 and S2 will
take the same time to travel to the point P and waves that emanate from
S1 and S2 in phase will also arrive, at the point P, in phase Thus, if the displacement produced by the source S1 at the point P is
given by
y1 = a cos wt
then, the displacement produced by the source S2 (at the point P) will
also be given by
y2 = a cos wt
Thus, the resultant of displacement at P would be given by
y = y1 + y2 = 2 a cos wt
Since the intensity is proportional to the square of the amplitude, the
resultant intensity will be given by
I = 4 I0
where I0 represents the intensity produced by each one of the individual
sources; I0 is proportional to a2 In fact at any point on the perpendicular
bisector of S1S2, the intensity will be 4I0 The two sources are said to
interfere constructively and we have what is referred to as constructive
interference