JohnRoth wrote:The formula applies to radiation from a point source. A laser is not a point source. For a laser, the "point source" is a very long way behind the laser itself. Trying to apply the formula using the distance from the laser is going to give you a very wrong answer.
kzt wrote:IIRC, a laser is a gaussian beam, and the spot size is linked to the beam waist, the wavelength (the Rayleigh length) and the range. If you assume the beam waist is the emitter and is multiple meters and the wavelength is say 0.1 nanometers you end up with absurd effective ranges. Like under 10 meter spot sizes at tends of millions of KM range. Like you can punch out the Manticore orbital stations from outside the hyperlimit kind of ranges.
When you go to longer frequency xrays and assume the waist is say twice that of the emitter rod (but the emitter rod in well under a millimeter) you get a much shorter maximum theoretical range.
Gentlemen forget the math...
Do the thought experiment!
A priori, the energy of the 'impulse' is contained in the wave front...
In the case of an omni-directional dispersion, such as a bomb blast, the wave front can be simplified as a spherical surface with a radius that increases over time; the energy of the impulse is fixed but the total area of the wave front increases as the wave front travels outward, therefore the mean energy density (unit of energy per unit of area) of the wave front decreases the farther the wave front is from its inception.
In the case of a focused dispersion, such as a laser of any wavelength, the wave front can be simplified as a 'bullet' from a gun barrel with the 'bullet' having the same cross-section as the barrel (for the sake of simplicity, I'm assuming the 'bullet' has negligible depth/length). Upon leaving the barrel the wave front begins to spread (like it is frangible/soft); it spreads as if it were a perpendicular slice of a cone whose axis is collinear with the gun barrel. Now, determining the focal point of that cone is a non trivial task; for e-m wave it involves: the e-m wave lengths being used, the gun barrel aperture, the gun barrel length, the aperture medium interface, the traveling media, and a few other esoteric parameters; suffice to say, a well built 'lasing' apparatus will have a focus point orders of magnitude longer than the barrel. Again the energy of the 'impulse' is fixed in the wave front as it exits the barrel at the aperture and the mean energy density decreases as the wave front travels onward (because the wave front is spreading). Reflective and inflictive apparatus are special cases of focusing - the reflective surface is in essence the aperture and you deal with the 'cone' directly without a 'barrel'; any 'lens' also will behave as an aperture with respect to the resultant wave front.
If you really want to do the math, then omni-directional dispersion will involve spherical formulas and focused dispersion will involve conical formulas.
The key thing in all cases is the amount of energy transferred to the target is ideally the occulted surface area of the target times the energy density of the wave front at the time of impact - the materials and the media involved will always attenuate the transfer (there is no perfect transfer).
One last thing, wave fronts are not just e-m waves, they can be: compression in media, particles in motion, and even grav waves; anything that can transfer energy!
Ok, I'm taking off my lecture's robes! Please forgive me, lecturing is a nee-jerk reaction for me and inspiring critical thinking is my compulsive disorder.
-David S.