Three coherent sources $S_{1}$ , $S_{2}$ and $S_{3}$ can throw light on a screen. With $S_{1}$ switched on intensity at a point P on the screen was observed to be $I$ . With only $S_{2}$ on, intensity at P was $2 I$ and when all three are switched on the intensity at P becomes zero. Intensity at P is $I$ when $S_{1}$ and $S_{2}$ are kept on. Find the phase difference between the waves reaching at P from sources $S_{1}$ and $S_{3}$ . (Answer in radians)

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Detailed Solution

Resultant intensity due to $S_{1} a n d S_{2}$ is I and adding third to this makes the resultant zero. This implies that intensity due to $S_{3}$ alone is I.
Amplitudes of waves reaching P from the three sources $S_{1}, S_{2} a n d S_{3}$ can be written as a, $\sqrt{2} a$ and a respectively. These three waves can produce zero resultant if phase difference between the first and third wave is $π / 2$ .