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Two parallel slits are illuminated by light composed of two wavelengths. One wavelength is lamA = 595nm. The other wavelength is lamB and is unknown. On a viewing screen, the light with wavelength lamA = 595nm produces its third-order bright fringe at the same place where the light with wavelength lamB produces its fourth dark fringe. The fringes are counted relative to the central or zeroth-order bright fringe. What is the unknown wavelength?
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Added Wed, 08 Jul '15
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Distance of the bright fringe from the zeroth order bright fringe = nlD/a

Distance of the dark fringe from the zeroth order bright fringe = (n-1/2)*lD/a

but D,a are equal for both wavelengths hence for equal spacing from the center:

n1*l1=(n2-0.5)*l2 (l1, l2 are wavelength)

3*595=3.5*(I2)

l2=510 nm
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