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?

 

[nlightner]

Double-slit interference is a phenomenon observed when a wave, such as light or sound, passes through two parallel slits and interferes with itself. The resulting pattern on a screen behind the slits shows alternating bright and dark fringes, with the brightest fringe corresponding to the central maximum.

In the case of m=2, this means that there are two bright fringes on either side of the central maximum. This does not necessarily mean that one wave is traveling 2 wavelengths longer than the other. Instead, it indicates that the two waves are in phase and constructively interfere at these points, resulting in a bright fringe.

The distance between the slits and the screen, as well as the wavelength of the waves, play a crucial role in the interference pattern observed. The exact mathematical relationship between these factors can be described by the equation d sinθ = mλ, where d is the distance between the slits, θ is the angle of diffraction, m is the order of the bright fringe, and λ is the wavelength of the waves.

In conclusion, the bright fringes observed in double-slit interference do not necessarily correspond to one wave traveling a specific distance longer than the other wave. Rather, they indicate regions of constructive interference where the waves are in phase and add up to create a bright spot on the screen.