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

Physics

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