How does the luminosity equation work?

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Discussion Overview

The discussion revolves around the luminosity equation L = 4 x Pi x b x d², focusing on its application in real-life scenarios, measurement techniques for distance and brightness, and the implications of the equation's components, particularly the role of 4Pi.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants express confusion about how to measure distance and brightness in practical situations, questioning the application of the luminosity equation.
  • One participant suggests that distance can be measured using various range-finding devices, while brightness can be measured with cameras or photo-diodes.
  • Another participant notes that rearranging the luminosity equation leads to the inverse square law, implying a relationship between brightness and distance.
  • Several participants discuss the surface area of a sphere, with one incorrectly stating the formula for volume, leading to clarification that surface area increases with the square of the radius.
  • Questions arise about how brightness decreases with distance, with some participants seeking clarification on the concept of brightness "falling off" as distance increases.
  • There is a mention of a hint regarding the inverse square law, suggesting that participants should explore this relationship further.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the luminosity equation and its implications. There is no consensus on the practical measurement methods or the conceptual understanding of brightness in relation to distance.

Contextual Notes

Some participants demonstrate uncertainty in their understanding of mathematical relationships, particularly between surface area and volume, which may affect their grasp of the luminosity equation.

IDK10
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I've read that L = 4 x Pi x b x d2
Where L = Luminosity (W)
d = distance (m)
b = brightness (W m-2)

But in a real life applied situation, how does it work, how does one measure the distance and its brightness? And what does the 4Pi do?
 
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IDK10 said:
I've read that L = 4 x Pi x b x d2
Where L = Luminosity (W)
d = distance (m)
b = brightness (W m-2)

But in a real life applied situation, how does it work, how does one measure the distance and its brightness? And what does the 4Pi do?
Hint -- what is the surface area of a sphere in terms of its radius? :smile:
 
IDK10 said:
But in a real life applied situation, how does it work, how does one measure the distance and its brightness?

The distance can be measured with a variety of range finding devices. You can probably do a google search and find plenty. The brightness can be measured using a camera, photo-diode, or other device.

Also, notice that if you move everything on the right over to the left except for brightness, you then get the well known inverse square law.
 
4/3 x πr3.

(I really wish you could easily do fractions)
 
berkeman said:
No, the surface area increases as r^2. Try again?

And you can use LaTeX to do fractions... https://www.physicsforums.com/help/latexhelp/
Oh, thought you meant volume, I saw you said surface area, then thought of volume for some reason. Don't ask why, the brain is weird. So, its the same as that, but instead of r2, its bd2.
 
IDK10 said:
b = brightness (W m-2)
So how does the brightness fall off with distance, and why?
 
berkeman said:
So how does the brightness fall off with distance, and why?
What do you mean by fall off with distance?
 
IDK10 said:
What do you mean by fall off with distance?
As you get farther and farther from the light source, it appears dimmer and dimmer, right?

Maybe do a search on the hint that Drakkith gave you... (actually he even gave you a link to the inverse square law)...
 
  • #10
berkeman said:
As you get farther and farther from the light source, it appears dimmer and dimmer, right?

Maybe do a search on the hint that Drakkith gave you... (actually he even gave you a link to the inverse square law)...
Oh, I meant a rephrasing, but I get what you mean.
 
  • #11
IDK10 said:
Oh, thought you meant volume, I saw you said surface area, then thought of volume for some reason. Don't ask why, the brain is weird. So, its the same as that, but instead of r2, its bd2.

The distance (d) is the same thing as the radius (r) since the object is considered to be at the center of a sphere and the observer (you or an instrument) is some distance from the center. You can write bd2 or br2.
 

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