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Dear experts,

I've been working at a problem for a while. If anyone can help, I'd really appreciate it. I'm working on refraction of an ultrasound beam as it crosses a planar interface between a Rexolite wedge and a steel sample block. I've got it mostly worked out, but am struggling with a (the) key parameter: How to define the (3D) vector after refraction across the plane. I can get the angle with relation to the plane-normal by Snell's Law, and I'm assuming the vector will be in the plane defined by the normal and the incident wave, and the line will contain the point at which it intersects the plane. This seems like it should be easy given the information I've already calculated, but I just can't seem to get the keystone in the top of the arch. 20140227-BeamPathWork-CloseUp.pdf

Can anyone help?

Thank You,

-Matt

I've been working at a problem for a while. If anyone can help, I'd really appreciate it. I'm working on refraction of an ultrasound beam as it crosses a planar interface between a Rexolite wedge and a steel sample block. I've got it mostly worked out, but am struggling with a (the) key parameter: How to define the (3D) vector after refraction across the plane. I can get the angle with relation to the plane-normal by Snell's Law, and I'm assuming the vector will be in the plane defined by the normal and the incident wave, and the line will contain the point at which it intersects the plane. This seems like it should be easy given the information I've already calculated, but I just can't seem to get the keystone in the top of the arch. 20140227-BeamPathWork-CloseUp.pdf

Can anyone help?

Thank You,

-Matt

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Start your 7-day free trialWhat are the numbers you are using when you get slightly different angles?

i=<0,0,1>

n=<1/Sqrt[2],0,1/Sqrt[2]>

r=0.73

I get <-0.28445, 0., 1.01465> which is 29.3 degrees from -n

If I use, Snell's Law:

Theta2 = 45 Degree;

Theta1 = ArcSin[Sin[Theta2]*0.73] = 31.1

I'm sure it's user error, but I'm searching for it.

Thanks again!

-Matt

Do you have a source, or are you deriving?

Thanks for the help!

n=<0.707106781186548,0,0.7

r=0.73

ir-n(ir·n-sqrt(1-r^2+(ir·n

-ir-n(-ir·n-sqrt(1-r^2+(-i

Is this what you got, and does it make sense with your conventions?

With

i={0,0,1}

n={0.70710678118655,0,-0.7

r=0.73

the ray that makes sense to me when I draw it is

ri - n(ri·n + sqrt(1 - r^2 + (ri·n)^2)) = {-0.240619517519044,0,0.97

Math / Science

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iand your unit normal isn,and the ratio of wavelength between the two media is

r,then your refracted ray will be

ri+n(rn·i-sqrt(1-r^2+(rn·i)^2)))