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# confused about reciprocity and law of reflection

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### #1lipsryme  Members   -  Reputation: 783

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Posted 26 June 2012 - 04:06 AM

I'm in need of a little clarification here.
As I understand the law of reflection states that the angle of the outgoing energy is the same as the angle of the incoming energy.
Now this is where its confusing to me as helmholtz reciprocity also states that the incoming and outgoing direction can be interchanged.

I don't really see the difference between what both are saying.

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### #2turch  Members   -  Reputation: 586

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Posted 26 June 2012 - 07:23 AM

The law of reflection states that an incoming light ray has a predictable outgoing ray when reflected. The Helmholtz reciprocity principle states that both the light ray and the outgoing ray (which can come from reflection or refraction) can be "reversed" - if a light ray from point A can get to point B, with a certain amount of flux, then if you shone that light from point B the same amount of flux would be measured at point A.

It basically means that a true one way mirror is impossible. You can't have light be able to pass one way through a medium but be blocked in the opposite direction. Similarly, it allows opposite forms of global illumination to be equivalent - you can calculate light by going from the lightsource to the camera, or you can calculate it by going from the camera to the light source, and if your calculations are correct, both methods will give the same results. The law of reflection has no effect besides describing what the angle of a reflected ray would be.

Edited by turch, 26 June 2012 - 07:30 AM.

### #3lipsryme  Members   -  Reputation: 783

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Posted 26 June 2012 - 07:49 AM

So basically Helmholtz is talking about the effect/result which is the same when changing both vectors and the Law of reflection is just stating the angle of the reflected/refracted ray?

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### #4turch  Members   -  Reputation: 586

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Posted 26 June 2012 - 12:12 PM

If by "changing both vectors" you mean swapping them (but keeping the angles the same) then yes.

The law of reflection doesn't apply to refraction, it only gives the angle of reflection. Helmholtz reciprocity applies to both reflection and refraction.

law of reflection : "1 + 2 = 3"
law of refraction (Snell's law) : "4 + 5 = 9"
Helmholtz reciprocity : "Addition is commutative"

So from the law of reflection and Helmholtz reciprocity, we can deduce that "2 + 1 = 3"

Edited by turch, 26 June 2012 - 12:13 PM.

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