(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In a double-slit experiment, He-Ne laser light of wavelength 633 nm produced an interference pattern on a screen placed at some distance from the slits. When one of the slits was covered with a thin glass slide of thickness 12.0 um, the central fringe shifted to the point occupied earlier by the 10th dark fringe. What is the refractive index of the glass slide?

Here's a link to a similar problem with a figure: www.physics.ohio-state.edu/~gohlke/pedagogy/Phys133I_Diffraction.pdf[/URL]

[b]2. Relevant equations[/b]

n=c/v; [itex]\Delta[/itex]x (constructive) = m[itex]\lambda[/itex] = dsin[itex]\Theta[/itex]; [itex]\Delta[/itex]x (destructive) = (m+1/2)[itex]\lambda[/itex] = dsin[itex]\Theta[/itex]; Snell's law (maybe?)

[b]3. The attempt at a solution[/b]

I understand that the glass slide will slow the passage of light, thus effectively increasing [itex]\Delta[/itex]x between the two light paths. I guess i need to figure out how many wavelengths the light going through the glass is "behind" the other beam. However, I don't understand how to incorporate this into the problem. It seems to get very complicated very quickly-- since the light isn't traveling straight through the glass, the distance is not equal to the thickness of the glass. Then, the light is refracted when leaving the glass, according to Snell's law. The only examples in my textbook were very simplistic, we didn't cover anything like this in class, and I'm really not sure what to do. I tried working out the problem as indicated in the link (though they solve for the thickness of the slide, and n is given), but got like -0.5 for n (and I was suspicious of their answer anyway, because it seems to neglect so many complicating factors). Can anyone help me think about this? Thanks a lot, sorry if this post is tl;dr :).

-CEP

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# Double-slit experiment, one slit covered with glass

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