huygens' principle

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RaSaaLa
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huygens' principle

Post by RaSaaLa »

Hey guys,
What is a point reflector and point diffraction (and point scatterer)?

GuyM
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Re: huygens' principle

Post by GuyM »

Huygens' Principle says that every point in a reflector can be considered to be a source of secondary wavelets.

So try this. Get a pencil, a ruler, a coin and a piece of paper.
- draw a straight line with the ruler, about 15cm long
- place the coin on that line, so that half is on one side, and half on the other
- draw round the coin, just on one side of the line, so you have a semi-circle
- move the coin along the line by 1 centimetre, and do it again
- repeat until you have a bunch of semicircles

Now, if you carried on doing this at smaller and smaller spacing, you'd have a lot of semicircles(!), and what you will see is a new "line" forming at one radius distance from the original line. If you imagine an infinite number of circles, that straight line would be perfect.

That's Huygens' construction. The circles are secondary wavelets, and in a real wave (not a pencil marks) all the parts of the semicircles add and combine destructively apart from constructed straight line - which is the new wavefront.

Now what would happen if instead of a line, you just had a dot o the paper, and centred the coin on that before drawing?
You'd only have the semicircle. No cancellation, just a secondary wavefront.

That's a point reflector or point scatterer - there's not enough of an object to form a planar reflected wave. You also see this where there's a sudden discontinuity in a sub-surface layer (like a fault); not enough destructive interference so we get a curved scattered wavefront not a reflection.

When the wind blows in the Dutch city of Leiden, little waves go along the surface of the many canals. They reflect, diffract and scatter off objects. In the museum there you can find Huygens' original manuscript. I stumbled across this many years ago and got quite excited - my wife and father-in-law thought I was nuts. Where I am going with this is look for lakes, pools and canals with ripples, even the sea, and watch how the waves diffract and scatter off objects. That's what Huygens did, and you will see all of this stuff happening!

Prospekteur
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Re: huygens' principle

Post by Prospekteur »

Very good explanation;-)

GuyM
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Re: huygens' principle

Post by GuyM »

I used to have a nice powerpoint slide illustrating this; it was animated and added in more and more circles centered on the same straight line until a new "wavefront" formed; that's back when I used to run seismic processing training courses :-)

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