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Consider an interference arrangement sim...

Consider an interference arrangement similar to YDSE. Slits `S_(1)` and `S_(2)` are illuminated with coherent microwave sources each of frequency 2 MHz The sources are synchronized to have zero phase difference. The slits are separated by distance d= 75m. The intensity `I_((theta))` is measured as a function of `theta` where `theta` is defined as shown in figure. if `I_(0)` is maximum intensity then calculated `I_((theta))` for `(i) theta= 0^(@), (ii) theta=pi//6 and (iii) theta = pi//2`

Text Solution

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Given `v=2` MHz`=10^(6)` Hz `d=75m`
As, `c=vlambda`
`rArrlambda=c/v=(3xx10^(8))/(2xx10^(6))=150m`
Path difference `Deltax=dsin theta`
Phase difference `theta =(2pi)/lambdaDeltax=(2pi)/lambdad sin theta=(2pi)/150xx75 sin theta`
`=pi sin theta`
Intensity at point P, `I=I_(0)cos^(2)(theta//2)=I_(0)cos^(2)((pisin theta)/2)`
`(i) theta=0, I=I_(0)`
`(ii) theta=pi/6=30^(@)`
`I=I_(0)cos^(2)((pi sin 30^(@))/2)=I_(0)cos^(2)(pi//4)=I_(0)/2`
`(iv) theta=pi/2=90^(@), I=0`
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