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Question
Obtain the equation for bandwidth in Young’s double slit experiment.
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Solution
- Condition for bright fringe (or) maxima:
The condition for the constructive interference or the point P to be have a bright fringe is,
Path difference, δ = nλ
where, n = 0,1,2,…….. ∴ `"dy"/"D"` = nl
y = `"n" (lambda"D")/"d"` (or)
`"y"_"n" = "n" (lambda"D")/"d"` - Condition for dark fringe (or) minima:
The condition for the destructive interference or the point P to be have a dark fringe is,
Path difference δ = (2n -1) `λ/2`
when, n = 1, 2, 3,………..
∴ y = `(2"n" - 1)/2 (lambda"D")/"d"` (or)
`"y"_"n" = (2"n" - 1)/2 (lambda"D")/"d"` - Equation for bandwidth:
- The bandwidth (β) is defined as the distance between any two consecutive bright or dark fringes.
- The distance between (n+l)th and nth consecutive brigh fringes from O is given by,
β = `"y"_("n + 1") - "y"_"n" (("n + 1")(lambda"D")/"d") - ("n" (lambda"D")/"d")`β = `(lambda"D")/"d"`
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