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The figure shows a modified Young's doub...

The figure shows a modified Young's double slit experimental set-up.
Here `SS_(2)-SS1=lamda//4.`
(a) Write the condition for constructive interference.
(b) Obtain an expression for the fringe width.

Text Solution

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(a) Initial path difference `=(lamda)/(4)+(x_(n)d)/(D)`
For constructive interference
Path difference `=nlamda`
`(lamda)/(4)+(x_(n)d)/(D)=n lamda" where "n=0, 1,2,3,4..`
`(x_(n)d)/(D)=nlamda-(lamda)/(4)=lamda(n-(1)/(4))`
(b) Fringe width `=x_(n)-x_(n-1)=lamda(n-(1)/(4))(D)/(d)=lamda[(n-1)-(1)/(4)](D)/(d)=(lamdaD)/(d)[n-(1)/(4)-n+1+(1)/(4)]=(lamdaD)/(d)`
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