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How to Find the Path Difference With Angle & Source Distance

When waves pass through an opening that is narrow compared to their wavelengths, they spread out in all directions even if they were traveling in a straight line before the opening. On the other side of the opening, the newly redirected waves interfere with each other, sometimes cancelling each other out, sometimes reinforcing each other. This phenomenon is called "diffraction." It is an important part of the study of optics, and also of the design of sound systems. The interference patterns generated by diffraction can be calculated by means of a quantity called "path difference."

Things You'll Need

  • Ruler or tape measure
  • Protractor
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Instructions

    • 1

      Measure the distance between the two wave sources if you were not given it as part of a homework problem. Though there is only one wave initially, once it passes through the aperture or apertures, it gets broken up into multiple waves. If you are analyzing the diffraction caused by two apertures, then this distance is the distance between the apertures. If you are analyzing the diffraction pattern caused by a single aperture, this distance will be the width of the aperture.

    • 2

      Measure the angle between the two waves at the place where they interfere if you were not given it as part of a homework problem. To do this, place one end of the ruler at the point of interference you are analyzing. Place the center of the protractor beneath it. Sight along the ruler to one of the wave sources. Mark the angle the ruler makes with the protractor. Repeat the procedure for the other wave source. Subtract the smaller angle from the larger one. The result is the angle between the waves.

    • 3

      Take the sine of the angle between the waves. Multiply the result by the distance between the sources. The result of this is the path difference, or the difference between the distances traveled by the two waves. For example, consider the case where you are studying double-slit diffraction between slits that are 3 cm across. At the point on the screen where they create an interference maximum, the angle between them is 30 degrees. The path difference is then three times sin(30), or 1.5 cm.


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