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# Appropriate conditions for looking at laser light without glasses?

#### Jiggel

##### New member
Hi guys, my first multi-watt laser arrived today, a 3W 445nm build by Lifetime17 (which I am very much enjoying, thank you Lifetime17!). I wear my Eagle Pair glasses whenever I operate the laser, but I have read in several threads here that it is safe to view even high-powered lasers when they are aimed far away at a (preferably dark) diffuse surface. I have never tried taking off my glasses, and I won't unless you guys confirm that it is indeed going to be 100% safe to do so. So with the safety stuff out of the way, this is my question: at what approximate distance would looking at a 3W laser dot with the naked eye be safe (assuming a near perfect Lambertian surface)?

I am no physicist, but I do have some experience programming light simulation algorithms, so I did some rough calculations. I encourage anyone to correct or expand upon this.

First, I will make a few assumptions for simplicity's sake:
Let's assume the angle between the direction of incoming radiance and the surface normal is exactly 0 degrees (this matters because of Lambert's cosine law). This means our laser is being shone at a flat surface at a 90 degree angle from the surface (straight on).
The next assumption is that the laser outputs 3W continuously. Lastly, we will assume our surface has an albedo of 0.1 at the 445nm wavelength (or whatever wavelength the laser is). This means we assume the surface is pretty black, but not as dark as something like ventablack.

Because our normal is aligned with our light direction, we can say that the angle of incidence is 0. Lambert's law tells us that the diffuse light reflection is proportional to the cosine of the angle of incidence. In our case it will be the cosine of 0, or 1. Next, we can calculate the perceived light brightness with an inverse square falloff attenuation function (the distance will represent the distance from our eyes to laser's dot). I chose inverse square falloff instead of a linear attenuation model because our laser dot can be treated as a point light source, and point lights have inverse square falloff. This is another assumption, because laser dots are not the same as point lights, but fuck it, it's probably close enough.

So, our formula is:
I = (dot product of N and L) * ((Li * kD) / (distance^2))
Where I is the radiant flux received by our eyes, N is the normal, L is the light angle, Li is the incoming radiance, kD is the diffuse reflection coefficient, and distance is distance (obviously). Since our normal is aligned with our incoming light direction (we are aiming the laser straight-on), our angle of incidence is 0, so the dot product becomes Cosine(0), or simply 1. Our function becomes:
I = (Li * kD) / (distance^2)
The variable kD represents the surface albedo, which is just the ratio of irradiance reflected to irradiance recieved. Our assumption is a ratio of 0.1, so our function now becomes:
I = (Li * 0.1) / (distance^2).

We can see from this function that the intensity of the laser will quickly drop the further you are standing from the dot.

PS: Sorry for the piss-poor notation, I do graphical programming as a hobby so I am writing this like I would be writing my code.

#### CurtisOliver

##### Well-known member
LPF Site Supporter
This is a classic case of over complication. A laser dot is a simple case of inverse square law, the only other thing to consider is the surface reflectivity as this will give off back reflection at greater intensity than that of the surrounding light. Then just factor in the AOI. Most high power lasers are safe to observe the dot from a distance, however it is unadvised due to the possibility of secondary reflection.

#### paul1598419

##### Well-known member
What Curtis has said is true. This is nothing more than a point source of light and, being such, behaves as the square of the distance it is away from you. I observe all my lasers against matte surfaces without goggle all the time. As long as you are sure the surface cannot reflect a collimated beam its intensity will decrease as the square of the distance it is away from you. An example of this is observing my 1100 mW 520nm laser at 10 feet and at 30 feet. This laser looks like a very bright light source at 10 feet, but at 30 feet it is not nearly as bright any longer.

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#### brendon7358

##### Active member
I have always preferred lower powered lasers because I can appreciate the color without worrying too much. Burning stuff gets old fast. Maybe get an lower powered 445nm with an osram diode? I think those are about 100mW great for pointing and as long as you don't point it at reflective surfaces no worries about your vision. And you can use your 3W laser with eye protection to burn stuff if you want. Or outside to appreciate all those photons (watch out for planes). Which is by the way the only way I personally recommend using lasers over about 2W without eye protection. Outside, pointing at the sky or far away trees.

##### Well-known member
LPF Site Supporter
Hi Jiggel,
Glad you received and are enjoying the build. glad you are asking questions about laser safety and wearing eye protection. There are other lower power single mode lasers available . The 520nm diodes are very visible even some lower power diodes. Foe instance here is a 160mw 520 build that is available. Enjoy and be safe always.

Rich

#### steve001

##### Well-known member
Hi guys, my first multi-watt laser arrived today,...
Definitely some overly complicated math.
Laser light at this output is dangerous when "specular reflections" enter ones eye. Other than that, the terminated beam spot will be just a bright light depending upon the color of the surface. I've viewed a 25 W argon laser spot reflecting off a light colored surface at about 60 feet. Though viewable it did become a bit uncomfortable after awhile do to much of the light reflecting back but that's all. Viewing closer to the spot at a greater oblique angle caused no problems. Experiment and avoid specular reflections.

#### Jiggel

##### New member
Thanks for the responses everyone! The general consensus seems to be that it is indeed safe from a reasonable distance.

I'd like to clarify that the math is there not for the purpose of proving that "it is probably safe to look at laser light from a reasonable distance", but rather as a shitty foundation for finding an approximate distance at which the light drops to 5mw or less. Which btw nobody has done yet, as the closest thing to an estimated distance is the handy chart Encap linked. Simplifying it down to inverse square attenuation doesn't give us anything useful other than what we already know...

The calculation is not particularly scientific or meaningful. It's just a matter of my own curiosity. I just thought it would be interesting to know.

#### Immo1282

##### Well-known member
LPF Site Supporter
The issue is that for practical purposes - as there are countless more significant factors here. We're talking about spherical cows on a frictionless plane in a vacuum, making assumptions that the beam is a perfectly collimated point-source

The level of cleanliness of the air will have a small effect, and more importantly the divergence! A 3W 445nm laser diode will have pretty high divergence, so at a significant distance your spot is going to be a larger area and therefore the power that will reflect is lower anyway.

Remember that lasers can be more dangerous than other light sources not because of their power - but because of the nature of the light. A 100W incandescent light bulb is not going to burn holes in your retina if you look directly at it because the light is not collimated. For the same reason, a matte surface that scatters the light in all directions is a safe target for you to look at at practically any distance.

Laser light is dangerous directly or from a specular reflection because the light enters your eye parallel, and your eyeball focuses it into a tiny spot on your retina. If 5mW of optical power was enough to blind us regardless of the nature of its source we'd all have been blinded from the moment we opened our eyes after birth!

I usually try and solve problems with practical explanations before I get the maths out - but it's interesting to see your take on it the other way round even though slightly misled in it's application!

#### Jiggel

##### New member
Thanks for the response Immo.
Divergence is trivial to incorporate into the model, and the assumption of a perfect vacuum won't significantly change results at these distances. However, you are correct that 5mW of parallel rays, such as those emitted from a laser, will be more dangerous than other light sources when hitting our eyes. So I should redefine my definition of "safe".

I guess I had too much stimulants when I made the post, because the more I think about it, the more assumptions there are. Even little details like how dilated the pupils are will matter, rendering the model useless. I should've thought it over longer before jumping to calculations and posting haha.
Cheers

#### Immo1282

##### Well-known member
LPF Site Supporter
I guess I had too much stimulants when I made the post, because the more I think about it, the more assumptions there are. Even little details like how dilated the pupils are will matter, rendering the model useless. I should've thought it over longer before jumping to calculations and posting haha.
Cheers
That's okay - Still good to see that you're thinking about safety in a detailed way. I was to explaining to my girlfriend the other month that sunglasses make lasers more dangerous as they barely block the beam and the pupils will dilate more with them on, allowing more light in! Little counter-intuitive things there that catch you out which are easily avoided with a proper model as you started in your thread.

I suppose in real terms this is the difference between maths/physics and the practical engineering approach - Instead of finding the threshold where something is safe to a high degree of precision, some are more comfortable getting a rough approximation and then building in a significant safety margin.

#### Benm

##### Well-known member
When looking at a dot the key issue is that the surface is actually matte.

If it is, the dot from a 3 watt 445 laser is no more intense than that of a 445 nm LED shining around a full 180 degrees, and would be safe to look at at armslength.

That said, few surfaces are actually that matte. Something like printing paper might actually not be that far off, but things like wallpaper can be somewhat reflective in specific directions, so you need to keep a big margin of error with that.

If you lust look at the beam sideways in clear air it's not likely to be dangerous at all, just make sure the beam is terminated safely or shines off into infinity without anything reflecting it back.

One realistic scenario for injury would be to shine a laser out of a house window and then look at the beam. You can do this safely but you need to be careful about the setup: a direct reflection from an average house window can be 4% of laser power, collimated and all, straight into your eyes. With a couple of watts that'd be eye damage before you can blink easily.

In my opinion looking at laser beams from the side is not dangerous, provided you get everything right: A stably mount laser, and a good beamstop or path to infinity where nothing reflective can make it's way in.

#### kecked

##### Active member
Z safest way to look at a laaaser iz with your eyes clozed....Sorry could not resist. (To be read with Dr. Ruth accent Or Arnold your choice)