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 = 645nm. The other wavelength is ?B and is unknown. On a viewing screen, the light with wavelength ?A = 645nm 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?

*Note: We're talking about the third, not fourth brignt fringe. Also, the dark fringes are at n+0.5 not at n-0.5.

Please be sure to show your work!

Explanation / Answer

This is Young's Double Slit Experiment, so we use the following equation:

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) = (4/3) 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) * (4/3) = Unknown Wavelength.

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