Two parallel slits are illuminated by light composed of two wavelengths. One wav

Question

Two parallel slits are illuminated by light composed of two wavelengths. One wavelength is A = 602nm. The other wavelength is B and is unknown. On a viewing screen, the light with wavelength A = 602nm 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? Please show all work and give answer. Not understanding this problem at all

Explanation / Answer

here,

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

lamdaA = 602 nm

then ,

602 * 3 = 9/2 * lamdaB

lamdaB = 401.33 nm

the unknown wavelength, lamdaB is 401.33 nm

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