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# How does Huygen's principal account for single-slit diffraction?

Question #67013. Asked by Bruce007. (Jun 15 06 10:56 PM)

elburcher

The principle as originally stated by Huygens does not account for diffraction.

http://www.mathpages.com/home/kmath242/kmath242.htm

 Jun 16 06, 7:27 AM
zbeckabee

"Consider the case of single slit diffraction, where we have one slit through which we shine light onto a distant screen. Suppose, we want to calculate at which point on the screen interference minima (dark stripes)occur. We then replace this relatively wide slit by an increasing number of narrow ones (subslits), and add waves produced by each. Obviousely, two small slits interfere destructively when their path lengths differ by ë / 2 (are in 180 phase difference). We can calculate (using phasors or a similar wave addition math) that for three waves from three slits to cancel each other the phases of slits must differ 120 degrees, thus path difference from the screen point to slits must be ë / 3, and so forth. In the limit of approximating the single wide slit with an infinite number of subslits the path length difference between edges of slit must be exactly ë to get complete destructive interference (and so a dark stripe on the screen)."

http://en.wikipedia.org/wiki/Huygens_principle

 Jun 16 06, 9:12 AM
elburcher

zbeckabee-

Your link is a refrence to The Huygens-Fresnel Principle, it came over 100 years after Huygens' original work.

 Jun 16 06, 1:25 PM
zbeckabee

Yes, I know. I posted it because I found it an interesting p.s. to your answer.

 Jun 16 06, 6:29 PM

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