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In the figures PO and QB are the extreme...

In the figures PO and QB are the extreme rays of a wavefront AB of monochromatic light of wavelength `lambda`. The value of angle `theta` for which the ray QB and ray OB interference constructively is

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`(AO)/(OB)= cos 2theta`
`AO= OB cos 2 theta` on reflection at O the ray suffers a phase difference of `pi` which is equivalent to a path difference of `(lambda)/(2)`. For constructive interference path difference should be `lambda`
`therefore AO+OB= (lambda)/(2)` for constructive interference
`OB cos 2theta +OB = (lambda)/(2)" "(d)/(OB)= cos theta`
`OB(1+cos 2theta)=(lambda)/(2)," "(d)/(cos theta)*2cos^(2) theta = (lambda)/(2)`
`cos theta = (lambda)/(4d) implies theta= cos^(-1)"" (lambda)/(4d)`.
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