Question

# Three coherent source kept along the same line produce intensity $${ I }_{ 0 }$$ each at point P on this line. When $${ S }_{ 1 }$$ and $${ S }_{ 2 }$$ are switched to simultaneously, intensity at point P is $${ 2I }_{ 0 }$$ Then

A
When S1 and S3 are switched on simultaneously, intensity at point P can be 2I0
B
When S1 and S3 are switched on simultaneously, intensity at point P can be 0
C
When all 3 sources switched on simultaneously intensity at Point P can be I0
D
When all 3 sources switched on simultaneously, intensity at point P can be 3I0

Solution

## The correct option is C When all 3 sources switched on simultaneously intensity at Point P can be $$I_{ 0 }$$Given, $$S_{1} = I_{0}$$$$S_{2} = I_{0}$$ $$S_{3} = I_{0}$$$$S_{12} = 2I_{0}$$ We know that $$S_{12} = I_{1} + I_{2} + \sqrt{I_1 I_2} \cos \theta$$ $$\Rightarrow 2I_{0} = 2 I_{0} + \sqrt{I_{0}^2} \cos \theta$$ $$\Rightarrow \cos \theta = 0$$ $$\boxed{\theta = 90^{\circ}}$$ $$S_{13} = 90 + 90 = 180^{\circ}$$ $$S_{13} = I_{2} + I_{2} + \sqrt{I_1 I_2} \cos \theta$$        $$= 2I_{0} - I_{0}$$        $$= I_{0}$$Correct option is CPhysics

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