Physics

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Can you please explain further because I don't understand?

Two parallel slits are illuminated by light composed of two wavelengths, one of which is 645 nm. On a viewing screen, the light whose wavelength is known produces its fifth dark fringe at the same place where the light whose wavelength is unknown produces its fifth-order bright fringe. The fringes are counted relative to the central or zeroth-order bright fringe. What is the unknown wavelength?

___________ nm

n*Lambda= xd/L

Now in this case, xd/l is a constant, so

n1*Lambda1= (n2-1/2)lambda2 if I follow the numbers right, then n1 is 5, lambda1 is 645nm, n2 is 5, and lambda2 is the unknown.

Notice in counting, the first dark fringe occurs before the first light fringe. So at the fifth light fringe, the fifth dark fringe is just before it.That is why I put the -1/2. Check my thinking on that, the wording has me a little bothered.

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