Question about the brightness of light and the inverse square law.

In summary, the brightness of light diminishes by 1/r^2. The unit of brightness is lumen. If you are 5 meters away from a light bulb and measure the brightness, then move 47 meters away and measure the brightness, the brightness would be 1/1764 less bright.
  • #1
zeromodz
246
0
Okay, I know that the brightness of light dims by 1 / r^2. I just need a little help about brightness and so forth. What exactly is the unit of brightness ? Also, when using 1 / r^2

Say I am 5 meters away from a light bulb and find the brightness, then I step back 47 meters. Would I just find the brightness by 47 - 5 = 42.

Then take 1 / 42^2 = 1/1764

So, then if I move 42 meters away it would be 1/1764 less bright. Then it would be from my original position?
 
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  • #2
Hi zero..you have the right concept, but the wrong math:

Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light.[1] In other words, brightness is the perception elicited by the luminance of a visual target. This is a subjective attribute/property of an object being observed.

http://en.wikipedia.org/wiki/Brightness

The radial lines of light, like those of gravitvy and electromagnetism from a point charge, decrease according to the area of a concentric sphere...4pi r2...

So you want the ratio of spherical areas at the two distances to determine the relative luminance...
1/(5)2/ 1/(47)2...which is NOT your calculated answer...

What would be the ratio in two dimensions? In one dimension??
 
  • #3
The lumen (symbol: lm) is the SI unit of luminous flux, a measure of the power of light perceived by the human eye. Luminous flux differs from radiant flux, the measure of the total power of light emitted, in that luminous flux is adjusted to reflect the varying sensitivity of the human eye to different wavelengths of light. The lumen is defined in relation to the candela by

1 lm = 1 cd·sr

That is, a light source that uniformly radiates one candela in all directions radiates a total of 4π lumens. If the source were partially covered by an ideal absorbing hemisphere, that system would radiate half as much luminous flux—only 2π lumens. The luminous intensity would still be one candela in those directions that are not obscured.
 

FAQ: Question about the brightness of light and the inverse square law.

What is the inverse square law?

The inverse square law is a principle in physics that describes the relationship between the brightness of light and its distance from the source. It states that the intensity of light is inversely proportional to the square of the distance from the source.

How does the inverse square law apply to light?

The inverse square law applies to light because light radiates outwards from a source in all directions, and as the distance from the source increases, the same amount of light is spread over a larger area, causing the intensity to decrease according to the inverse square of the distance.

Can the inverse square law be applied to all types of light?

Yes, the inverse square law can be applied to all types of light, including natural light from the sun, artificial light from light bulbs, and even light from stars in outer space. It is a fundamental principle that governs the behavior of light.

How does the inverse square law affect the brightness of light sources?

The inverse square law states that as the distance from a light source increases, the intensity of the light decreases. This means that the further away you are from a light source, the dimmer it will appear. Conversely, the closer you are to a light source, the brighter it will appear.

Is the inverse square law the only factor that affects the brightness of light?

No, the inverse square law is not the only factor that affects the brightness of light. Other factors such as the size and intensity of the light source, the material of the object the light is shining on, and atmospheric conditions can also impact the brightness of light. However, the inverse square law is a significant factor in determining the brightness of light at different distances from the source.

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