provides some pertinent background information for this problem. Two parallel sl

Question

provides some pertinent background information for this problem. Two parallel slits are illuminated by light composed of two wavelengths. One wavelength is A = 593nm. The other wavelength is B and is unknown. On a viewing screen, the light with wavelength A = 593nm 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

when you have a bright fringe, the optical path difference that we will call delta equals the order * lambda
when you have dark fringe, the optical path difference equals (the order +1/2) * lambda

if you consider the same place on the screen, delta doesn't change which means deltaA = 3 * lambdaA = lambdaB = (4+1/2)* lambdaB
so lambdaB = 2/3* lambdaA = 395.33 nm

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