Manufacturers of wire (and other objects of small dimensions) sometimes use a laser to continually monitor the thickness of the product. The wire intercepts the laser beam, producing a diffraction pattern like that of a single slit of the same width as the wire diameter; see the figure. Suppose a He-Ne laser, wavelength 632.8 nm, illuminates a wire, the diffraction pattern being projected onto a screen 2.65 m away. If the desired wire diameter is 1.37 mm, we have to calculate the distance between the two tenth-order minima on each side of the central maximum.
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Solution: Click For PDF Version From the Babinet’s principle we expect that the intensity pattern on the screen due to diffraction from the wire will be equivalent to that from a slit of width equal to the diameter of the wire. The position of the minima of diffraction pattern is given by the relation
where
As the angles
where
Therefore, the distances of the 10th minima on either side of the principal shadow will be
We thus find that
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is the diameter of the wire and
is the wavelength of the light used for producing the diffraction
pattern.
will be small, we use the approximation
is the distance of minima from the principal shadow, and D
is the distance of the screen from the wire.
