It's one of several customary ways to express phenomena that have logarithmic properties. Sound pressure and sound power being two, and electromagnetic phenomena being another.
Every time you post, we get a clearer picture of your knowledge level. The term "decibel" is not restricted to measuring sound levels and is often used for electrical, radio and optical power.
Decibel: 1. A dimensionless measure of the ratio of two powers, equal to 10 times the logarithm to the base 10 of the ratio of two powers P1/P2.
It means that as R grows the attenuation grows exponentially
Yes and you can use that formula to calculate the amount of attenuation. It isn't much at all in clear air. He used an attenuation coefficient between clear air and haze just to be fair. He calculated that a laser beam would be attenuated to 40% of it's original strength over five miles.
Wow, congrats on discovering Beer's law.
You have the correct form ie exp(-alpha*distance),but you are simply failing to realize that alpha is quiet small at certain, indeed, many wavelengths.
This is why there are laser radars with multiple kilometer ranges and COIL anti-missle systems that have successfully downed missles and GuideStar sodium beacons that provide a reference spot at the sodium layer, etc, etc.
Look, you know a thing or two for a nonspecialist but you really should conduct yourself with a bit more civility when discussing areas of which you obviously have no first hand experience.
Because decibels (tenths of a Bel) is a ratio of power.