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In an Young's experiment, the distances ...

In an Young's experiment, the distances between two slits and that between slits and the screen are 0.05 cm and I m respectively. Find the distance between `3^(rd)` bright and `5^(th)` dark fringes. Take the wavelength of light equal to `5000Å`

Text Solution

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Here, d = 0.05 cm, D = 100 cm,
`lamda=5000Å=5xx10^(-5)cm`,
`x._(5)-x_(3)=?`
n = 5 (dark) and n = 3 (bright)
For `n^(th)` bright fringe,
`(x_(n)d)/(D)=nlamda`
Taking n=3
`(x_(3)d)/(D)=3lamda`
`:.x_(3)=(3lamdaD)/(d)" "....(1)`
For `n^(th)` dark fringe,
`(x._(n)d)/(D)=(2n-1)(lamda)/(2)`
Taking n=5
`(x._(n)d)/(D)=(9lamda)/(2)`
`:.x._(5)=(9lamdaD)/(2d)" "....(2)`
Now, `x._(5)-x_(3)=(9lamdaD)/(2d)-(3lamdaD)/(d)=(3lamdaD)/(2d)`
`=(3xx5xx10^(-5)xx100)/(2xx0.05)`
`:.x._(5)-x_(3)=15xx10^(-2)cm=1.5mm`
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