# Single slit interference. ?

1. Jul 22, 2009

### wavingerwin

Single slit interference. ??

Can someone please explain to me about the single slit interference phenomenon?

My teacher said that after passing through the slit, it can be modeled that there are two wave source coming form each end of the "wall" which makes the slit. How can this actually happen?

Diagram:

| |
| |
--- top end of the 'wall'

>>> direction of wave

--- bottom end
| |
| |

And also, does this happen in every wave (e.g water ripples, sound waves) or just electromagnetic wave?

Thanks

2. Jul 22, 2009

### Staff: Mentor

Re: Single slit interference. ??

The single-slit interference pattern is actually produced by interference among the waves that come from all points across the width of the slit (not just the endpoints). So in order to calculate the details of the interference pattern (i.e. the intensity at each point on the screen) you have to perform an integration. You can find the details in any optics textbook at the intermediate level or above, e.g. Hecht, Pedrotti, Meyer-Arendt, Strong, ...

For calculating only the locations of the minima (zero intensity) you can use a simplified non-calculus argument, which depends on exact cancellation of matched pairs of waves. This leads to a result which can be described using only the waves at the two edges of the slit, if I remember correctly.

3. Jul 22, 2009

### wavingerwin

Re: Single slit interference. ??

does this happen in every wave (e.g water ripples, sound waves) or just electromagnetic wave?

Furthermore, what if the slit width is exactly the same as the wave's wavelength?
does interference can happen still? Or it only produces a continuous band with a maxima at the center?

Thanks

4. Jul 22, 2009

### Born2bwire

Re: Single slit interference. ??

Single slit interference requires slits larger than a wavelength. Like jtbell states, a rough approximation is to consider that the wavelets passing though the middle of the slit are unperturbed, it is only the wavelets at the edges of the slit that will diffract and be the main contributors to an interference pattern. Once the slit's width becomes on the order of or smaller than the wavelength then you will reproduce a single slit diffraction pattern.

5. Jul 22, 2009

### wavingerwin

Re: Single slit interference. ??

By "a single slit diffraction pattern" does it mean it produces a continuous band or a series of bright and dark fringes?

thanks