If UV radiation 1 cm away from the halogen bulb is equal to Sun's radiation, what is the level of radiation 1 meter away?

Halogen light bulbs emit some amount of UV radiation, and some sources consider them dangerous. Here it is written, that UV radiation (of certain types) from a particular halogen bulb was equal to the Sun's at the Earth's surface, if measured 1 cm away from the bulb.

Assuming the bulb emits radiation equally in all directions (it probably does), do I understand correctly that the level should fall proportionally to the distance from the bulb? If there is only small fraction of the Sun's radiation remaining just 1m away, so the bulb is probably safe to use if used in a normal way.

Would this change in any way if the bulb is not a point source but has a filament of say, 1 cm length (assuming "distance" as the distance from the closest part of the filament)?

The quoted document refers to medical radiation dose, in terms of intensity of radiation absorbed by tissue. In your case, the Sun's radiation is taken at the Earth's surface.

Since intensity is inversely proportional to square of distance from source, it will be actually $0.01\%$ of the Sun's radiation intensity in the ultraviolet region at the Earth's surface as you are standing $100$ times further away from the source (so the intensity becomes ${1/10^{4}}^{th}$ of that at $1 cm$ from the source).

Also, if we treat the bulb filament as a cylinder, intensity becomes inversely proportional to distance from the bulb. For the dimensions and distance you mentioned, you can consider the bulb filament as a point source (it is a $1 \%$ error for this assumption, below a usually acceptable $5 \%$ error threshold). Otherwise, at 1m away, the intensity will be $1\%$ that of the quoted case.

Whether this intensity is safe or not, I'm not entitled to comment as I have no idea of biological radiation thresholds. A radiologist could help you.

• The $1/r$ falloff applies to a long cylinder (i.e. one significantly longer than your distance from it). A light bulb filament, at distances of over $1\,{\rm cm}$, is well approximated by a point source (i.e. the $1/r^2$ falloff rule applies). – Ilmari Karonen Oct 27 '15 at 18:30
• The law becomes inverse square when the size of the filament can be ignored: from about 5 filament diameters on it is an excellent approximation, and even before that it is not too bad - better than a 1/r assumption. Google "electric field finite line charge" for equations. – Floris Oct 28 '15 at 13:08
• OP assumed a filament of length 1 cm, thus @IlmariKaronen 's comment is not applicable. However, for Floris, I will edit to clarify – Tamoghna Chowdhury Oct 28 '15 at 13:49
• Good point, a 1 cm filament at a distance of 1 cm is in the transition region where neither 1/r nor 1/r² is a very good approximation of the falloff. But still, the range from 1 cm to 1 m lies mostly in the 1/r² region, so the intensity at 1 m will be about 1/10,000 = 0.01% of the intensity at 1 cm. It certainly won't be anywhere near 1/100 = 1%. – Ilmari Karonen Oct 28 '15 at 15:57

The intensity goes as $r^{-2}$, not $r^{-3}$. One meter is 100 times further away than 1 cm, thus 1/10,000th the intensity.

Side Note 1
How often are you within 10 cm (~3.94 inches) of a halogen bulb? The article states that 15 minutes under constant exposure at 10 cm can elicit erythema. However, who sits under a halogen bulb 10 cm away for 15 minutes straight (ignoring tanning beds)?

Side Note 2
Basic silica glass is opaque to most of the UV spectrum, so just cover the bulb with glass, stay more than 10 cm away, avoid prolonged exposure at short distances, and direct the light onto a surface (e.g., a desk) instead of directly on you.

• Wasn't this supposed to be the physics SE? – Tamoghna Chowdhury Oct 27 '15 at 13:10
• And he said 10cm. Why does your answer involved 1m? – Tamoghna Chowdhury Oct 27 '15 at 13:11
• The article describes people with the known disease, they are highly sensitive to UV and cannot be safely exposed to the normal sunlight (unlike other people). I only use the "1 cm" information from that source. – h22 Oct 27 '15 at 13:45
• Ok. Thank you for addressing the second part of the question, which I couldn't – Tamoghna Chowdhury Oct 27 '15 at 14:06
• I have a halogen desk lamp that has a silica glass cover for (I believe) just this reason. The bulb itself is fused Quartz and transparent in the near UV but the cover is a UV filter. – Floris Oct 28 '15 at 13:10

While the first inclination is to drag out inverse square laws of point sources ... you have to take into account the surface area of the exposure. The radiation is fairly constant. a 1 cm sphere would receive the same level of radiation as a 1 meter sphere. what would change is the radiation per square cm. when looking axially the halogen filament could be considered a point source. and now it is time to drag out the inverse square law.

IMHO halogens are a health and fire hazard. and super inefficient. destroy and discard immediately. replace with LEDs. 100Watteqiv. 14 watts real, cool to the touch after 100 hours of operation.

• Interesting perspective but I am pretty sure that UV radiation dose damage is not linear. Also once you are a meter away most of the light will not hit your body, period. The question was about intensity not damage so I think the other answers are OK. As for the "health and fire hazard" opinion: while you are entitled to your opinion we like our answers to be fact based if possible. You have energy consumption facts - but health hazards?? – Floris Oct 28 '15 at 13:14