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Two identical narrow slits S(1) and S(2)...

Two identical narrow slits `S_(1)` and `S_(2)` are illuminated by light of wavelength `lambda` from a point source P. If, as shown in the diagram above the light is then allowed to fall on a scree, and if n is a positive integer, the condition for destructive interference at Q is that

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The correct Answer is:
3
For constructive interference `Deltax=mlambda`
`(4)/(3)sqrt(d^(2)+x^(2))-sqrt(d^(2)+x^(2))=mlambda`
`(1)/(2) sqrt(d^(2)+x^(2))=mlambda`
`x^(2)=9m^(2)lambda^(2)-d^(2)`
`p=3`
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