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Two parallel slits are illuminated by light composed of two wavelengths. One wavelength is λA = 643nm. The other wavelength is λB and is unknown. On a viewing screen, the light with wavelength λA = 643nm produces its third-order bright fringe at the same place where the light with wavelength λB produces its fourth dark fringe. The fringes are counted relative to the central or zeroth-order bright fringe. What is the unknown wavelength?

?2021-04-01T12:55:45Z

Favorite Answer

For constructive interference, d*sinΘ = mλ
and for destructive interference, d*sinΘ = (n+½)λ
(and for "fourth order," n = 3)

d*sinΘ is the same for both of our wavelengths, so
3 * 643nm = 3½ * λB
meaning that λB = 551 nm

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