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Diffraction Patterns

  1. Feb 27, 2014 #1
    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 [itex]\frac{a}{2}[/itex]?Are there any diffractions occur when the point source having the distance of [itex]\frac{a}{3}[/itex],[itex]\frac{a}{4}[/itex] 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. jcsd
  3. Feb 27, 2014 #2

    BvU

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    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##
     
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