Bringing light to the subject of Welding and the damage caused if eye protection isn’t used.
The same welding arc is seen a half block away. These are the same level of irradiance at the retina. The spot on the retina is much smaller in the second case, but the watts per square cm on the retina are the same. The same damage can occur, but only in a smaller spot.
Now it is true that a much smaller spot on the retina is affected, but since your eye is always moving around, shifting the image, you can still damage a lot of retinal tissue. Therefore moving 500 meters away did not reduce the irradiance (brightness in layman terms) on the retina! You probably need to be several km away to be safe, where the welder’s arc is just a pinpoint, as small as a star seen from Earth. The Rayleigh scatter of the atmosphere will probably be a significant factor in reducing the ultraviolet intensity in the image in your eye at this distance.
If the welding arc is smaller, say only a couple of cm, (much smaller than in the photos) then the r-squared losses begin sooner, say about 100 meters. Up to that point, only Rayleigh scattering is reducing the intensity. That is not enough. I would never look at a welding arc from less than 10 km away without an appropriate filter. Distance is not a reliable way to reduce the intensity unless you are absolutely certain that the arc is small compared to your eye’s resolution.
EDIT: Because of the large number of comments concerning “arc eye” or “flash burn” I have come to realize that most people think that this injury is the only eye injury associated with welder’s arcs. There is a misconception that the cornea and lens absorb all the harmful ultraviolet light. While it is true that the cornea and lens do absorb a lot of the UV, they do not absorb it all, so a very bright source like a welder’s arc or the sun (viewed directly or in a specular reflection) is still very dangerous not only from the standpoint of visible light but also of ultraviolet. Because the cornea absorbs the lion’s share of the ultraviolet, it receives painful damage. This misleads people into thinking this is the only damage. I was unaware that so many people believed that. Let me try to correct this misunderstanding. There are three mechanisms of eye damage from a welding arc:
1. Flash burn – this is essentially sunburn, but on the cornea of the eye. This is usually repaired in a few days naturally, but it can be painful, and it can get infected. It is normally treated with dilating eye drops, antibiotics, and an eye patch. Since this is painful, people notice right away and seek treatment.
2. Photo-induced cataracts – the short wavelength light (440 nm and less) can induce changes in the lens which cause it to cloud up. The effects are cumulative and irreversible. Typically, it takes a lifetime of exposure to produce cataracts. However, working around welding without sufficient eye protection can greatly accelerate the process. The only treatment for cataracts that I am aware of is to remove the clouded lens and replace it with a plastic one. Cataracts are not painful and take a long time to develop. People do not always associate their cataracts with welding arcs, so it is not a common complaint.
3.Retinal damage – this causes permanent blind spots on the retina as cones and their nerve connective tissue are destroyed. This is the greatest danger to bystanders who try to look at the welding arc from a distance and misapply the inverse square law. I thought that this was the type of injury that the question was getting at. There is no treatment to reverse blind spots on the retina. The eye never completely repairs this type of damage. What repair the body does is with about a 1-month half-life. Most of the repair that you ever get is within the first couple of months after exposure. However, the brain does adapt and does not notice the blind spot after a while. After initial exposure, the person does not feel much pain and is not likely to seek immediate medical attention. Of the three types of injury, the first is by far the one most patients seek attention for. This is because the effect is both immediate and painful. The patient knows what caused the injury. Although 2 and 3 are far more serious, 1 is the only one likely to get reported and treated.
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