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Reflection off of a surface

  1. Nov 25, 2014 #1
    I am writing a simulation in MATLAB of particles that perfectly reflect off of a surface. However, my question is physics based, not code based.

    So here is my issue. A particle is traveling towards a flat plane in space at z=1 with a velocity vector of [0,0,1]. The normal vector of the surface is [0,0,-1].

    I want to calculate the reflected trajectory of the particle so I use the following expression.

    [tex]|\vec{v}|\left[2(\hat{n} \cdot \hat{v})\hat{n}-\hat{v}\right][/tex]

    The problem is, in my head, the reflected trajectory should clearly be [0,0,-1] However, when I calculate it, I get [0,0,1]. Why is this happening? Is my equation right?


    I know the normal vector of the surface is correct, as the front of the plane is facing the particle source.

    Also, I need to use the general expression for a reflection as I will be moving onto any 3D object as the next step.
    Last edited: Nov 25, 2014
  2. jcsd
  3. Nov 25, 2014 #2
    Draw the vectors and their versors for a generic incident beam, let's say at 30° wrt the surface.
    Then draw the projection of versor v on the direction of n, and its double.
    Then sum it to the negative versor of v using the parallelogram rule.
    You have to use a ruler to have the proportions right.

    It appears that the result is opposite to the reflected beam. Do you agree?
  4. Nov 25, 2014 #3


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    I'm not sure where you got the equation from. Break up your initial velocity vector into a lateral component and a normal component. Reverse the normal component, and add it back to the lateral component. It should work regardless of the direction of the normal.
  5. Nov 25, 2014 #4

    It seems like I get the opposite of what I should get. But I already got this result using the simpler case of a vector normal to the plane.


    I remember in many of my electromagnetics courses, there was a general expression for the reflection of a vector. I looked on the internet to try and find it and got this..


    Scroll down to "Reflection across a line in the plane"

    The result of the equation doesn't seem to match my intuition.


    I will look into using MATLAB functions to project the normal then subtract as another way of doing this without the equation.
  6. Nov 25, 2014 #5


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    Try manually deriving the reflection by breaking it up into components. Maybe the wiki is wrong (I didn't check).
  7. Nov 25, 2014 #6
    So everything points to there being a negative sign that is wrong. I swapped the negative sign and it works in one scenario in my code, but not another. I will determine if this problem is really solved or if something is weird in my code and report back!
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