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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 `S S_(2)-S S_(1)=lambda//4`.

(a) Write the condition for constructive interference.
(b) Obtain an expression for the fringe width.

Text Solution

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The path difference `S_(2)P-S_(1)P=[(y_(n)d)/(D)+(lambda)/(4)]`
For constructive interference , path difference `=n lambda`,
Where `n = 0,1,2,3,….. `
`[(y_(n)d)/(D)+(lambda)/(4)]=n lambda`,
So, position of nth bright fringe is `= y_(n)=(n-(1)/(4))(lambda D)/(d)`
Fringe width`beta=y_(n)-y_(n-1)`
Or `beta=(lambda D)/(d)`
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Knowledge Check

  • The fringe width in Young’s double slit experiment increases when

    A
    Wavelength increases
    B
    Distance between the slits increases
    C
    Distance between the source and screen decreases
    D
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    `(lambda)/(theta)`
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