Interactive LearningWare 27.1 provides some pertinent background information for

Question

Interactive LearningWare 27.1 provides some pertinent background information for this problem. Two parallel slits are illuminated by light composed of two wavelengths. One wavelength is ?A = 568nm. The other wavelength is ?B and is unknown. On a viewing screen, the light with wavelength ?A = 568nm produces its third-order bright fringe at the same place where the light with wavelength ?B produces its fourth dark fringe. The fringes are counted relative to the central or zeroth-order bright fringe. What is the unknown wavelength?

Explanation / Answer

position of dark fringe: xn = (n-1/2)(L?/b)
position of light fringe: xn' = n(L?/b)
now x2 = (2-1/2)(L?/b) = (3/2)(L?/b)
x7' = 7(L?'/b)
and x2 = x7'
so 3?/2 = 7?'
?' = 3?/14 = 3*568/14 nm = 121.71nm

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