# Homework Help: Diffraction Patterns

1. Feb 27, 2014

### haha1234

1. The problem statement, all variables and given/known data

Is it necessary that a single slit diffraction occur with the two source having the distance of $\frac{a}{2}$?Are there any diffractions occur when the point source having the distance of $\frac{a}{3}$,$\frac{a}{4}$ and so on?
And I would like to know whether are there only destructive interference occur?

2. Relevant equations

3. The attempt at a solution

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2. Feb 27, 2014

### BvU

Hi Ha,
There are no two sources in the drawing; there is only the one slit opening that is imagined to be subdivided into two "sources" that are deemed a/2 apart. As you correctly suspect, it is equally well possible to subdivide into 3, 4, 5, etc. sources (with successively smaller extension / width) that interfere constructively at greater and greater angles. In the resulting intensity pattern the angles in between have destructive interference.

The intensity at a given point on the screen is in fact an integral over the slit opening. See e.g. Fraunhofer diffraction or Single slit diffraction.

The resulting intensity pattern is ${\sin^2 x \over x^2}\$; $\ \ \ {\sin x \over x}$ has been found to be important enough to get its own name: ${\rm sinc}\ x$