Interactive LearningWare 27.1 explores the approachtaken in problems such as thi

Question

Interactive LearningWare 27.1 explores the approachtaken in problems such as this one. Two parallel slits areilluminated by light composed of two wavelengths, one of which is664 nm. On viewing the screen, the lightwhose wavelength is known produces its third dark fringe at the same place where where thelight whose wavelength is unknown produces its fourth order bright fringe. The fringes are countedrelative to the central or zeroth order bright fringe. What is theunknown wavelength?

the unknown wavelength is
1nm

Explanation / Answer

we have the condition for darkfringe as dsin = (m+1/2)* for third dark fringe m = 2 sin = (2+1/2)* /d-------(1) we have the condition for brightfringe as dsin = m* for fourth bright fringe m = 2 sin = 4'/d ------(2) we have the condition for brightfringe as dsin = m* for fourth bright fringe m = 2 sin = 4'/d ------(2) equating the two equations we have (2+1/2)* =  4'/d or ' = (2+1/2)* /4            =2.5*664 nm /4            =415nm Hope this may help you .

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