# Does brightness of the light remains constant with the variation of the distance with respect to the source in vaccum?

I have this question going in my mind from many days, i.e why brightness of light emitted from any light source around us decreases with distance? The brightness of light from tube light, streetlight, etc or any light from any source around us, decreases with the distance. As my teacher has taught me that light is a form of radiation, I thought this decrease in brightness may be due to absorption of radiation in the medium. I don't know whether it is correct or wrong. If it is wrong, please explain why there will be decrease in brightness of light with increase in distance from the light source?
If we assume that decrease in brightness of light is due to absorption of radiation in the medium, then in vaccum (where we can assume no energy dissipation), would there be no decrease in brightness of light with respect to distance from the light source?

• en.wikipedia.org/wiki/Inverse-square_law explains it quite well. Dec 19, 2013 at 23:31
• The brightness has to decrease, otherwise the space, that is full of stars will be too bright May 11, 2016 at 14:20

## 3 Answers

It's because the amount of area "covered" increases as the square of the distance. Imagine a sphere, centered on the source, at a radius equal to your eyeball's location. If the source generates X watts (or whatever unit you like) total, the brightness, i.e. the percent of light which hits your eyeball, is X divided by the ratio of your eyball's area to the area of the sphere. Now move back a few meters. Your eye's area is the same but the sphere's area has increased dramatically. Thus the amount of light, or watts, hitting your eye has gone down.

Absorption makes things worse, of course, but is not necessary for the light your eye sees to decrease. There are plenty of exceptions to the inverse-square rule, e.g. collimated laser source, but this should cover your question.

• Thank you for the answer sir. If I would had given a chance to choose two answers as best, I would had accepted yours also. Dec 20, 2013 at 13:20

No, in a vacuum light sources will appear dimmer as you move further from them because of the inverse square law. In a medium, a light source suffers from both the inverse square law and absorption/scattering. Below is a diagram illustrating the inverse square law:

As you move further away from a light source, your pupil (assume it remains the same size, though it does dilate in dark conditions) represent a smaller area of the spherical shell representing the distance from your light source. Essentially, this means you detect fewer photons with your eye from the source than you would have if you were much closer. This is the reason why astronomers have absolute and apparent magnitudes - they have to adjust brightnesses (magnitudes really) of objects in order to make any sort of fair comparisons.

Also think about this: If the brightness of light sources in a vacuum didn't change with distance, why is our sun the brightest astronomical object we observe? There are many stars which are intrinsically much brighter than the sun, yet in actuality they come nowhere close.

• I can't remember who it was that I saw the film years ago as part of the "PSSC Physics Course" who imagined that automatic toast buttering machine squirting butter out isotropically and thus showed your argument above this idea. So the movie youtube.com/watch?v=JW3tT0L2gpc is not an original idea, and likely grounded on this PSSC physics film made in the 1960s which I recall (I sought rather later than the 1960s BTW). Dec 20, 2013 at 4:17
• @astromax. Thank you for the answer. I learnt about inverse square law from your answer, and now I am able to understand how in practical brightness or illumination decreases. Dec 20, 2013 at 13:15
• @WetSavannaAnimalakaRodVance Great video - thanks for the pointer. VINAY Glad you found my answer illuminating - no pun intended. Dec 20, 2013 at 14:56

Well just what do you mean by "Brightness." There is no such unit of measurement in the field of Photometry. A more appropriate and meaningful term is "Luminance" measured in Lumens per steradian, per square meter, or alternatively, in Candela per square meter; since the candela is one lumen per steradian.

And Luminance is a property of a light source; so it does not vary at all, with distance from the light source.

Now if you meant "Illuminance" or illumination instead of luminance, then that falls off with the inverse square of the distance, and is the lumens per square meter, or "lux" falling on a distant surface. It is NOT a property of a light source itself.

You need to learn and use the correct terms, if you want to talk about any branch of science. "Brightness" is not among them ; that is a concept of perception.

• Yes I agree, brightness is a relative term. Though in astronomy we usually have standard stars and the like to compare to (traditionally the star Vega, though there are other systems). Brightness is usually interpreted as meaning 'magnitude'. Dec 20, 2013 at 1:06
• This seems to be more appropriate as a comment than an answer. Dec 20, 2013 at 1:23
• Then you should re-read my ANSWER again. And note that I said the LUMINANCE of a light source does NOT change with distance from the source; so my answer to the question was NO. If you mean some other photometric unit of measure for "brightness" which I explained is NOT a photometric quantity, then please say so, so we can all understand what you mean. Dec 20, 2013 at 18:59