How Does m=2 Affect the Path Difference in Double-Slit Interference?

[lha08]

Homework Statement

I was just wondering in double-slit interference, when it's a bright fringe, let's say m=2, does that mean that one wave coming from one of the slits is traveling 2 wavelengths longer than than the other wavelength coming from the other slit? How does that work?
Thanks

Homework Equations

The Attempt at a Solution

 

[Redbelly98]

Homework Statement

I was just wondering in double-slit interference, when it's a bright fringe, let's say m=2, does that mean that one wave coming from one of the slits is traveling 2 wavelengths longer than than the other wavelength coming from the other slit?

Yes, that's exactly what it means.

How does that work?
Thanks

It works because the waves coming out of the slit travel at some angle, so that one of the paths is longer. See the figure here:
http://commons.wikimedia.org/wiki/File:Double_Slit_Experiment.png

Hope that helps?