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Two beams of light having intensities I and 4I intefere to produce a fringe pattern on a screen. The phase difference between the beams is `pi // 2` at point A and `pi` at point B. Then the difference between the resultant intensities at A and B is

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Resultant intensity `I=I_(1)+I_(2)+2sqrt(I_(1))sqrt(I_(1))cosphi`
Resultant intensity at point A is `I_(A)=I+4I+2sqrt(I)sqrt(4I)cos((pI)/(2))=5I`
Resultant intensity at point `B,I_(B)=I+4I+2sqrt(I)sqrt(4I)cos2pi=9I(becausecos2pi=1)thereforeI_(B)-I_(A)=91-51implies41`
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