How Do You Determine the Exact Phase Difference in Single Slit Diffraction?

[jegues]

Homework Statement

See figure attached.

Homework Equations

The Attempt at a Solution

$$\Delta L = asin\theta = m \lambda$$

If the waves are in phase, we would expect L to me a integer number of wavelengths, when they are out of phase, L should be an odd number of wavelengths, but when I compute,

$$\frac{\Delta L}{\lambda}$$

I get neither an integer nor an odd number. This tells us that the waves must be somewhere inbetween being completely in phase or completely out of phase, but how do I find the exact result?

 

[vela]

The problem doesn't say the point on the screen corresponds to a maximum or minimum, so there's no reason to expect the two waves to be out of phase by a multiple of half a wavelength.

The problem is asking you to find the phase difference between the two waves. What causes the waves to arrive with different phases?

 

[jegues]

The problem doesn't say the point on the screen corresponds to a maximum or minimum, so there's no reason to expect the two waves to be out of phase by a multiple of half a wavelength.

The problem is asking you to find the phase difference between the two waves. What causes the waves to arrive with different phases?

The path length difference, isn't it?

 

[vela]

Yup, so what you want to do is find the path length difference and translate that into a phase difference.

 

[jegues]

Yup, so what you want to do is find the path length difference and translate that into a phase difference.

Okay, well I showed in my first post that I know how to get the path length difference, so how do I make the translation into a phase difference?

 

[vela]

Oh, sorry, I didn't get what you getting at in your first post.

Every time the path length difference increased by wavelength λ, the phase difference increases by 2π.

 

[jegues]

Oh, sorry, I didn't get what you getting at in your first post.

Every time the path length difference increased by wavelength λ, the phase difference increases by 2π.

Ahhhh! That's the key I was missing, so the answer is C correct?

 

[vela]

That's what I get.