# Simple radio wave reflection question

1. Jul 16, 2007

### iewgnem

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.

thanks.

2. Jul 17, 2007

### Danger

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.

3. Jul 17, 2007

### lalbatros

Well,

"... 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
4. Jul 17, 2007

### xez

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:
http://en.wikipedia.org/wiki/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:
http://en.wikipedia.org/wiki/Mie_theory

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:
http://en.wikipedia.org/wiki/Electromagnetic_modeling

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.

5. Jul 17, 2007

### xez

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

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

6. Jul 17, 2007

### xez

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).

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.

7. Sep 21, 2010

### jago25_98

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...