# Question about the inverse-square law and lasers **URL:** \ **Category:** Factual Questions\ **Created:** [January 10, 2017, 12:56am UTC](https://boards.straightdope.com/t/question-about-the-inverse-square-law-and-lasers/776789 "2017-01-10T00:56:08Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![Crafter\_Man](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crafter_man/32/458_2.png) [@Crafter\_Man](https://boards.straightdope.com/u/Crafter_Man)\ **Post date:** [January 10, 2017, 12:56am UTC](https://boards.straightdope.com/t/question-about-the-inverse-square-law-and-lasers/776789/1 "2017-01-10T00:56:08Z")
On the wiki page for the [inverse-square law](https://en.wikipedia.org/wiki/Inverse-square_law#Light_and_other_electromagnetic_radiation) it says, > [@](#): > > For non-isotropic radiators such as parabolic antennas, headlights, and lasers, the effective origin is located far behind the beam aperture. If you are close to the origin, you don’t have to go far to double the radius, so the signal drops quickly. When you are far from the origin and still have a strong signal, like with a laser, you have to travel very far to double the radius and reduce the signal. I find this interesting, as I had thought very directional beams like flashlights and lasers did not obey the inverse-square law. Apparently the inverse-square law applies to _anything_ that transmits an electromagnetic wave. At any rate, my question is specifically about the statement, “the effective origin is located far behind the beam aperture.” For a typical laser, _where_ is the effective origin? Is it a few inches behind the laser? A few feet? A few miles? ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [January 10, 2017, 1:22am UTC](https://boards.straightdope.com/t/question-about-the-inverse-square-law-and-lasers/776789/2 "2017-01-10T01:22:45Z")
It depends on a lot of factors, like the aperture, frequency, “mode”, and some other stuff. The minimum possible divergence for a laser is given by: theta = (2 \* wavelength) / (pi \* aperture) If we project backwards, imagining a virtual point source, we have (for small theta): theta \* origin = aperture And so: origin = (pi \* aperture[sup]2[/sup]) / (2 \* wavelength) So a 5 mm aperture @ 450 nm would have a virtual origin 78 meters behind the exit (optimally). In practice, it’ll be a fraction of that; perhaps 1/3 for a typical laser. ---
**Author:** ![Crafter\_Man](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/crafter_man/32/458_2.png) [@Crafter\_Man](https://boards.straightdope.com/u/Crafter_Man)\ **Post date:** [January 10, 2017, 11:28am UTC](https://boards.straightdope.com/t/question-about-the-inverse-square-law-and-lasers/776789/3 "2017-01-10T11:28:04Z")
Excellent! Thank you. I assume the same technique can be used for antennas with parabolic reflectors? ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [January 10, 2017, 1:35pm UTC](https://boards.straightdope.com/t/question-about-the-inverse-square-law-and-lasers/776789/4 "2017-01-10T13:35:36Z")
Your ideal and minimum-dispersion laser beam is a TEM[sub]00[/sub] Gaussian Beam, with an intensity profile that follows a curve that looks like a normal distribution curve. The isophot “contour lines” of such a beam have hyperbolic forms, with the beam being its narrowest at the “beam waist”: > **[Gaussian beam](https://en.wikipedia.org/wiki/Gaussian_beam)** > > In optics, a Gaussian beam is a beam of electromagnetic radiation with high monochromaticity whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity (irradiance) profile. This fundamental (or TEM00) transverse Gaussian mode describes the intended output of most (but not all) lasers, as such a beam can be focused into the most concentrated spot. When such a beam is refocused by a lens, the transverse phase dependence is altered; this... You can sort of view the beam as virtually collimated over a length called the Rayleigh Range on either side of the waist (as shown in the Wikipedia article). Beyond that, the beam to a good approximation expands in a cone defined by the angle **Dr. Strangelove** gives. The “origin” of that angle is at the beam waist. This is the way laser beams are often presented in classes, but you should note that you general, run-of-the-mill laser beam is actually composed of a multiplicity of modes, and that all but the TEM00 expand more rapidly than this, and have more complex shapes. You can generate a true Gaussian beam, but you generally need to use pinhole filters or the like to guarantee it. Nevertheless, assuming a Gaussian beam is usually a pretty good assumption for doing calculations about your laser beam. Not always. Some lasers have atrociously non-Gaussian profiles and propagation characteristics, in particular a lot of nitrogen lasers and excimer lasers (Some of which aren’t even truly “lasers”, since they lack proper feedback and cavities). ---
**Author:** ![md2000](https://avatars.discourse-cdn.com/v4/letter/m/73ab20/32.png) [@md2000](https://boards.straightdope.com/u/md2000)\ **Post date:** [January 10, 2017, 6:31pm UTC](https://boards.straightdope.com/t/question-about-the-inverse-square-law-and-lasers/776789/5 "2017-01-10T18:31:33Z")
The inverse-square law still applies. The question is - at what angle does your bean spread? If your cat is chasing a quarter-inch dot 10 feet from the laser, but at 30 feet it’s twice the diameter - then that describes an angle of spread. the “effective origin” is where the beam would start from if that angle was from a (virtual) point source. Double the distance from the “effective source” and The area is 4 times, the intensity per square inch is half - inside the beam… ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [January 10, 2017, 7:21pm UTC](https://boards.straightdope.com/t/question-about-the-inverse-square-law-and-lasers/776789/6 "2017-01-10T19:21:00Z")
> [@CalMeacham](#): > > Your ideal and minimum-dispersion laser beam is a TEM[sub]00[/sub] Gaussian Beam, with an intensity profile that follows a curve that looks like a normal distribution curve. The isophot “contour lines” of such a beam have hyperbolic forms, with the beam being its narrowest at the “beam waist”]… “Isophot”: I understand the word (particularly given its pedagogic context), but as usual just checking: shorthand?; or term of art only in laser study; term of art in wider physics? ---
**Author:** ![Leo\_Bloom](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/leo_bloom/32/10377_2.png) [@Leo\_Bloom](https://boards.straightdope.com/u/Leo_Bloom)\ **Post date:** [January 10, 2017, 7:28pm UTC](https://boards.straightdope.com/t/question-about-the-inverse-square-law-and-lasers/776789/7 "2017-01-10T19:28:49Z")
> [@md2000](#): > > The inverse-square law still applies. The question is - at what angle does your bean spread? > > If your cat is chasing a quarter-inch dot 10 feet from the laser, but at 30 feet it’s twice the diameter - then that describes an angle of spread. the “effective origin” is where the beam would start from if that angle was from a (virtual) point source. Double the distance from the “effective source” and The area is 4 times, the intensity per square inch is half - inside the beam… I take your point about thinking in a cat scenario, but it is valid only if he is chasing a chimera of a reflected light in air-born dust particles shown directly normal to his vision (facing out, unless you’re a sadist), because, as I suspect, he or she cannot fathom foreshortening of anything on that pointillistic surface. (Elsewhere in SD I have mentioned my own visual experiences with this.) On the floor, or wall, or other more irregular surface such as your wife’s lap, the cat chases a projected ellipse of one form or another predicated on that spread-out diameter. Or so I gather.