This is question number 7P in chapter 27 in Cutnell and Johnson\'s Physics 8th E

Question

This is question number 7P in chapter 27 in Cutnell and Johnson's Physics 8th Edition. A very good solution can be found there, there is just one part of the solution that 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 third dark fringe at the same place where hte light whose wavelength is unknown produces its fourth-order bright fringe. The fringes are counted relative to the central or zeroth order bright fringe. What is the unknown wavelength?

Here is a link to the solution http://www.chegg.com/homework-help/physics-8th-edition-chapter-27-problem-7p-solution-9780470223550

Can anyone explain to me why m=2 is used for the 3rd order fringe? Using m=3 produces the wrong answer, I tried it.

Explanation / Answer

Eq 1) (Order of Fringe x Wavelength) / Slit Separation = Fringe Seperation / Slit-Screen Separation. By looking at the first fringe only for both wavelengths we can satisfy the criteria given in the question by setting: Eq 2) Fringe Seperation (Unknown) = (7/2) Fringe Separation (645nm) We also simplify the first equation by looking for the fringe seperation (set order to 1): Eq 3) Wavelength / Slit Separation = Fringe Seperation / Slit-Screen Separation. Rearrange this to find Fringe Seperation and impose the condition (Eq 2). Assume the setup is the same for both wavelengths (i.e. Slit-Screen Separation and Slit Separation are the same for both wavelengths) and equate. This should give you: (645nm) * (7/2) = Unknown Wavelength.

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