I’ve been playing with my new green laser pointer (way cool, BTW), and thinking about how the beam spreads. An ordinary point source radiating into a sphere follows the inverse-square law, where the intensity of the light gets reduced by 4 every time the distance from the light source doubles.
It seems to me that the laser doesn’t follow this law ( the light is being radiated in a very narrow cone), hence it is visible a LONG ways away.
What equation describes intensity vs distance for a laser?
Ordinary light propagates in spherical waves. Laser light (at least if you’ve got a nice, well-behaved one) propagates in Hermite-Gaussian wavefronts. The lines of equal intensity relative to the center describe hyperbolic paths, so that for relatively short distances (called the Rayleigh Range) the beam is effectively parallel and collimated. Outside this range, the beam starts to spread out in a cone, and the inverse square law holds.
How big is the Rayleigh Range? It’s inversely proportional to the wavelength of the light and proportional to the square of its smallest diameter (the beam “waist”)
See here, for instance:
The far-field angle is proportional to the wavelength and inversely proportional to the beam waist, so if you “squeeze” the beam down to a really small size, it “blows up” really fast. Paradoxically, if you enlarge the beam waist (by putting it through a telescope, for instance, or a judiciously-positioned lens), the beam will have a larger rayleigh range and seem to be parallel for longer.
Those laser pointers have the problem that the beam is generated in an extremely small region, so it starts out small, and would rapidly balloon out and be useless as a pointer. In addition to this, it measures different sizes along the two directions (it’s elliptical rather than round). To correct for both problems, diode laser beams are typically passed through an asymmetric lens (or two effectively crossed cylindrical lenses) to make the beam larger (so it has a bigger Rayleigh range) and to equalize the twi axes, making the beam round.
All of this is done in an incredibly tiny length. Most of the laser pointer barrel is taken up by the batteries.