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(a) Why are coherent sources necessary t...

(a) Why are coherent sources necessary to produce a sustained interference pattern ?
(b) In Young's double slit experiment using monochromatic light of wavelength `lamda`, the intensity of light at a point on the screen where path difference is `lamda`, is K units. Find out the intensity of light at a point where path difference is `lamda//3`.

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(a) Coherent sources have constant phase difference between, i.e., phase difference does not change with time. Hence, the intensity distribution on the screen remains constant and sustained.
(b) `I=4I_(0) cos^(2) (phi)/(2)`
`I_(0) to ` incident intensity
`I to ` resultant intensity
At a point where, path difference `=lamda`
`phi=(2pi)/(lamda)xx lamda=2pi`
Putting in (i) `K=4 I_(0) cos^(2) pi`
`K=4 I_(0) implies I_(0)=(K)/(4)`
At a point where, path difference is `(lamda)/(3)`
`phi=(2 pi)/(lamda)Delta x =(2 pi)/(lamda)(pi)/(3)=(2pi)/(3) implies I_(2)=4 I_(0) cos^(2) ((phi)/(2))=4((K)/(4))cos^(2)((pi)/(3))=4(K)/(4)xx(1)/(4)=(K)/(4)`
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