# Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the beams is p/2 at point A and p at point B. Then the difference between the resultant intensities at A and B is: Option 1) 2I Option 2) 4I Option 3) 5I Option 4) 7I

Resultant Intensity of two wave -

$I= I_{1}+I_{2}+2\sqrt{I_{1}I_{2}}\cos \theta$

- wherein

$I_{1}=$ Intencity of wave 1

$I_{2}=$ Intencity of wave 2

$\theta =$ Phase difference

$I_{A} = I+4I+2\sqrt{I.4I}.\cos \frac{\pi }{2} =5I$

$I_{B} = I+4I+2\sqrt{I.4I}.\cos \pi =I$

$I_{A}-I_{B} = 4I$

Option 1)

2I

Incorrect

Option 2)

4I

Correct

Option 3)

5I

Incorrect

Option 4)

7I

Incorrect

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