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Simple radio wave reflection question

  1. Jul 16, 2007 #1
    heres a simple question I somehow couldn't find an answer on the internet.

    we know radio waves only reflect (significantly) when it strikes an object with size greater than the wavelength, but I'm not sure what exactly defines the "size" of the object.

    For example, if I were to confine a 1m wavelength wave to a beam of only 0.5 meter diameter, if the beam strikes a 2 meter long, but only 0.1m in diameter rod placed perpendicular to the beam, will the beam reflect.

    Another way to put it is, when we talk about "size" greater than the wavelength, are we talking about the absolute size, or the size of the surface being exposed to radiation.

  2. jcsd
  3. Jul 17, 2007 #2


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    Gold Member

    Welcome to PF, Iewgnem. This is not at all along the lines of my knowledge, so I'm just going to give you my opinion. To start with, only the profile that intercepts the waves can be considered. Anything else might as well not be there.
    The other thing is that, to the best of my recollection, the reflecting surface must be a multiple or particular fraction of the wavelength, rather than just the wavelength itself. That's the limit of my input, and it might be wrong.
  4. Jul 17, 2007 #3

    "... if I were to confine a 1m wavelength wave to a beam of only 0.5 meter diameter ..."

    such a beam would diverge very fast and after a few meters, it could be several meters in diameter.

    Read about diffraction and you will be able to estimate the divergence of the beam.
    The divergence depends not only on the width of the beam but also on the intensity distrubution within the beam.
    Gaussian beams have a Gaussian intensity profiles and these are the beams that diverge the least.
    But still Gaussian beams diverge, and a lot if their cross-section is not much larger than the wavelength.
    Gaussian beams are common in many applications from laser experiement to radars.
    Last edited: Jul 17, 2007
  5. Jul 17, 2007 #4


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    Hmm well this gets into lots of fields.

    When the scattering particle is a lot smaller than the
    wavelength of the radiation you can model it with
    Rayleigh scattering:

    When the particle/object scattering is any size, e.g.
    comparable to or larger than a light wavelength you
    can look at it as Mie scattering:

    When you deal with scattering from objects that are
    complex in geometry or materials and
    are significant in size relative to a wavelength
    (e.g. some reasonable fraction of a wavelength to several
    wavelengths in size), you can try to use an integral
    equation type modeling technique to model the interaction
    of the surface geometry of the object and the field.
    One common type of model is MOM or Method Of Moments
    based on integral equation formulation.

    You can also use FDTD of Finite Difference Time Domain
    modeling which looks at the time-domain propagation of
    an E/M wave at a resolution of a fraction of a wavelength
    in size and a fraction of a cycle in duration and
    numerically evolves the propagation according to the
    maxwell's equations.

    You can use FEM (Finite Element Method) based models
    to discretize the volume of the space in which the wave
    propagates and again model the time domain propagation
    in terms of time-steps that are a fraction of the wave
    cycle time.

    For objects that are complex in materials and geometry
    and especially ones involving electrical conductors
    you often find that they set up induced resonance
    patterns and traveling waves that cause non-uniform
    radiation scattering versus angle of incidence and angle
    of observation.

    For objects very much bigger than the wavelength
    you can start to look at it in an optical analogy and
    use GTD (geometric theory of diffraction) and PO
    (physical optics) type models to essentially look at the
    ways you get shadows, diffraction zones/patterns,
    specular reflection, refraction, etc. just as you'd expect
    with light interacting with large objects.

    Look here:

    And here:

    It sounds like you're sort of talking about the RCS
    (Radar Cross Section) figure of the effective physical
    'cross section' an object has relative to its scattering
    effectiveness of an E/M wave of a given frequency.
    For many simple shapes (cylinder, sphere, plate, et. al.)
    the RCS is known analytically and simple equations can
    be used to estimate what the RCS values will be.
  6. Jul 17, 2007 #5


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    Code (Text):

    From a couple of references I happen to have the following data for objects
    much larger than a wavelength:

    RCS of fundamental shapes adapted from Barton

    wvl = wavepength
    pi = pi = 3.141...
    d = diameter
    L = length of cylinder or Dipole
    r = radius

    Shape of Object                 Max RCS         Min RCS         # LOBES         Width of Major Lobe

    Sphere (pi*d >> wvl)            pi*d^2/4        pi*d^2/4        1               2*pi radians

    Ellipsoid (a,b >> wvl)          pi*a^2          pi*b^4/a^2      2               approx. b/a

    Cylinder (L, r >> wvl)          pi*d*L^2/wvl    0               8L/wvl          wvl/L

    Flat Plate (Area >> wvl^2)      4*pi*A^2/wvl^2  0               8L/wvl          wvl/L

    Dipole (L = wvl/2)              0.88*wvl^2      0               2               pi/2

    Cylinders (right circular cylinders are considered here) have a peak
    broadside antenna-like gain proportional to their length in wavelengths, assuming
    both the circumference and the length are much larger than the wavelength.

    G_cyl = pi * L / wvl
          G_cyl = the "gain" of the cylinder
          L = the length of the cylinder
          wvl = the wavelength

    A_cyl = d * L
          A_cyl = a cylinder's broadside projected area
          d = its diameter

    From [a previous equation] and assuming perfect conduction
    (i.e. perfect metal conductive cylinder material), the peak
    broadside RCS of the cylinder is:

            br_rcs_cyl = pi * d * L^2 / wvl

  7. Jul 17, 2007 #6


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    BTW I forgot to mention that the MATERIAL of the object
    has a very significant effect on the scattering.

    Electromagnetic waves classically will ALWAYS
    partially reflect and refract and absorb whenever there's
    a discontinuity, however small (above quantum sizes)
    in the medium in which they propagate.

    If the refractive index (which is basically
    identical to specifying the permittivity and permeability)
    of the material does not change, the wave can proceed
    without interference. That's why some kinds of glass
    are 'invisible' when stuck under-water or clear oil since
    the refractive index of one material (glass) is very closely
    equal to the refractive index of the other material (water
    or oil).

    If your cylinder was made of something like diamond with
    a very high refractive index, and it was immersed in
    air then it'd have a relatively strong scattering because
    of the larger discontinuity in the properties of the medium.

    Whereas if the material was made of styrofoam
    which have refractive indices for radio waves much closer
    to air, it'd barely cause any scattering.

    As before, materials that are good electrical conductors
    can't admit electric waves into their interiors (i.e. the
    E field tangential to the conductor is zero), so electric
    currents get induced that cause E/M waves that
    travel along the surface of the conductor until they hit
    discontinuities and reflect or until they wrap around the
    object or whatever, and these traveling surface waves
    and any excited resonances have the effect of scattering
    and re-radiating the incident EM wavefront.

    You can imagine a mirror polished metal that's made into
    such a sub-wavelength cylinder, and see intuitively
    that you'll still have some scattering from it, even though
    it's less than a wavelength in radius and diameter.
  8. Sep 21, 2010 #7
    Thought it better to necro this than start a new thread?

    If this creates scatter... then perhaps waves can be reflected round obstructions...
    I think of this in terms of helping get a satelite signal in awkward locations... but I wouldn't expect that to work what with it being such a weak signal... in that situation anyway...
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