1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Law of reflection

  1. Aug 26, 2009 #1
    1. The problem statement, all variables and given/known data

    An electromagnetic wave is incident upon a planar interface at an oblique angle [tex]\theta_i[/tex], where it is reflected. For the wave vector components parallel to the interface, we have [tex]k_{xi}=k_{xr}[/tex]. Thus, [tex]\theta_i=\theta_r[/tex]. The wave numbers for the incident and reflected waves are equal. Find the relation between the wave vector components normal to the interface for the incident and reflected waves.


    2. Relevant equations

    [tex]\cos\theta_i=\cos\theta_r[/tex]

    See attached picture.


    3. The attempt at a solution

    Thus, from the picture, [tex]\frac{k_{zr}}{k}=\frac{k_{zi}}{k}\Longrightarrow k_{zr}=k_{zi}[/tex].

    To me this seems to imply that both normal components point in the same direction, in addition to being of the same magnitude. But shouldn't the normal components have opposite signs, since the incident and reflected waves travel in opposite normal directions?
     

    Attached Files:

  2. jcsd
  3. Aug 26, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi _Andreas! :smile:

    (have a theta: θ and try using the X2 tag just above the Reply box :wink:)
    I don't understand how you get kzr/k = kzi/k :confused:
     
  4. Aug 27, 2009 #3
    Hi!

    It follows from cosθi=kzi/k and cosθr=kzr/k, since θir and k=|ki| = |kr|.
     
  5. Aug 27, 2009 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Perhaps I'm misunderstanding your picture, but isn't cosθi = -kzi/k ? :confused:
     
  6. Aug 27, 2009 #5
    Uhm... can you explain how you get this result?
     
  7. Aug 27, 2009 #6

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    kzi points right? :confused:
     
  8. Aug 27, 2009 #7
    Sure, but that's in the positive z direction.
     
  9. Aug 27, 2009 #8

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    ah, then isn't cosθr = -kzr/k ? :confused:
     
  10. Aug 27, 2009 #9
    I guess so, and there's my problem. I tend to think of kzr without the sign as the z component of kr.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Law of reflection
  1. Laws of Reflection (Replies: 1)

  2. The law of reflection (Replies: 1)

Loading...