Original poster: Jim Lux <jimlux@xxxxxxxxxxxxx> At 08:30 PM 2/8/2007, you wrote:
Original poster: <davep@xxxxxxxx>
>...Inverse Square 'law'...
Welllllll.
And i am NOT proposing New Physics.
Really.
8)>>
"inverse quare' is The Law FOR OMNIDIRECTIONAL sources.
That's for ANY radiative source with any directive properties when you are in the far field.
Each unit radius out from the source the energy gets
'spread more widely', becomes 'thinner'. (To put it in
non mathematical terms.)
However.
Ponder, please, a 'Very Well Collimated' beam.
Parallel. BIG 'reflector', meaured in wavelengths.
The beam (laser, microwave) does not get bigger.
I believe this was the concept for the 'rectenna'
driven concept.
Still have inverse square law, the power is not evenly distributed over the sphere. But, make the sphere twice as big, and for any spot along a line from the center of a sphere, the power density at the bigger sphere will be 1/4 of that at the smaller.
The exception is when you are in the "near field" where the distance to the source is small compared to the physical extent of the source. And, that's because the observation point is no longer effectively the "same" distance from all parts of the source. If you were to break the big source up into many smaller sources, the contribution from each of the smaller sources would vary with inverse square of the distance from that smaller source, and the net effect is the sum of all those smaller sources. (aka Huygen's principal)
Even a well collimated beam (e.g. from a laser) has measureable divergence. 0.5 milliradian would be a very well collimated beam from a small gas laser. Most diode lasers (like a laser pointer) would be around 2 mrad.
You can figure out how good it can possibly be by the "diffraction limit", which relates the wavelength of the radiation with the size of the aperture. (roughly = 1.22 lambda/d) For instance, that small gas laser might have a 1mm beam at 0.628 nm, so it's about 1600 wavelengths across. (diffraction limit = 0.75 mrad) The big 70 meter antennas at the Deep Space Network are about 1900 wavelengths across at 8.4 GHz, or about 0.6 mrad. At 32.05 GHz, it's about 0.15 mrad. (this tells you how accurately you have to point that big antenna to, for instance, communicate with a Mars Rover) 1 mrad is about 3 arcminutes.
You could take that laser and run it through a small telescope, say with a 15 cm aperture, and get a very well collimated beam. (5 microradian!) but it's still spreading as it goes far away. Yes, if you are only a couple meters away, it will appear that inverse square doesn't hold, but that's because you are still too close.
And that limit (where the far field approximation is valid) is roughly at a distance of 2 d^2/lambda (d=diameter) (about 72 km for the laser and the 6" telescope) and about 275 km for the DSN 70 meter antennna at X-band.
Now no real beam will beperfect, but, maybe,
close enough for 'all practical purposes'.
best
dwp