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 x9I cos π2Ip = 10 IIQ = I + 9I + 2I x 9I cosπ= 10 I - 6I = 4 I∴ Ip - IQ = 10 I - 4 I = 6 I

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 x9I cos π2Ip = 10 IIQ = I + 9I + 2I x 9I cosπ= 10 I - 6I = 4 I∴ Ip - IQ = 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 $\frac{π}{2}$ 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

7 I

6 I

answer is B.

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Detailed Solution

$I_{p} = I + 9 I + 2 \sqrt{I x 9 I} \cos \frac{π}{2}$

$I_{p} = 10 I$

$I_{Q} = I + 9 I + 2 \sqrt{I x 9 I} cosπ$

= 10 I - 6I = 4 I

$∴ I_{p} - I_{Q} = 10 I - 4 I = 6 I$

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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 9I 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 :