The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is π2 at point P and π at point Q. Then the difference between the resultant intensities at P and Q will be:

IP=I+9I+2I⋅9I cosπ2=10 I IQ=I+9I+2I⋅9I cosπ =I+9I+2⋅3I×−1=4 I So, IP−IQ=10I−4I=6I

The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is π2 at point P and π at point Q. Then the difference between the resultant intensities at P and Q will be:

IP=I+9I+2I⋅9I cosπ2=10 I IQ=I+9I+2I⋅9I cosπ =I+9I+2⋅3I×−1=4 I So, IP−IQ=10I−4I=6I

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The two light beams having intensities $I$ and $9 I$ interfere to produce a fringe pattern on a screen. The phase difference between the beams is $\frac{π}{2}$ at point P and $π$ at point Q. Then the difference between the resultant intensities at P and Q will be:

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$2 I$

$5 I$

$6 I$

$7 I$

answer is B.

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$I_{P} = I + 9 I + 2 \sqrt{I \cdot 9 I} \cos \frac{π}{2} = 10 I I_{Q} = I + 9 I + 2 \sqrt{I \cdot 9 I} \cos π = I + 9 I + 2 \cdot 3 I \times - 1 = 4 I S o, I_{P} - I_{Q} = 10 I - 4 I = 6 I$

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The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is π2 at point P and π at point Q. Then the difference between the resultant intensities at P and Q will be:

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The two light beams having intensities $I$ and $9 I$ interfere to produce a fringe pattern on a screen. The phase difference between the beams is $\frac{π}{2}$ at point P and $π$ at point Q. Then the difference between the resultant intensities at P and Q will be: