Homework Help Forum: Physics

Posted by Marissa on Thursday, November 5, 2009 at 5:39am.

Microwaves with λ = 1 mm are incident upon a 10 cm slit. At a distance of 1 m from the slit, what is the width of the slit's image? The answer is supposed to be 10 cm. I can't seem to get that though. Can someone explain?

• Physics - drwls, Thursday, November 5, 2009 at 11:06am

  The pattern beyond the slit is usually not called an image; it is called a diffraction pattern. At this close range, you may be dealing with near-field Fresnel rather than conventional Fraunhofer scattering. You need to review the differences and apply the correct formulas, which are quite complex for Fresnel scattering. (λ/D) is rather small in this case (0.01), so I expect there to be a bright spot about 10 cm wide 1 m beyond the slit, with some fringes at the edges. I just don't have enough time to review all this for you. Sorry

  
  

• Physics (correction) - drwls, Thursday, November 5, 2009 at 11:16am

  Apparently your book answer agrees with mine, but I should have used the terms Fresnel and Franhofer DIFFRACTION, not scattering. The type of diffraction that you have depends upon the dimensionless ratio D/sqrt(λ R) If the ratio is <1, you have Fraunhofer scattering with uniformly spaced light and dark bands. In your case that ratio is much larger than 1. Most radiation will follow geometrical-optics ray paths to the near field screen

  
  

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