How does the luminosity equation work?

[IDK10]

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?

 

[berkeman]

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?

 

[Drakkith]

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.

 

[IDK10]

4/3 x πr³.

(I really wish you could easily do fractions)

 

[berkeman]

4/3 x πr3.

(I really wish you could easily do fractions)

No, the surface area increases as r^2. Try again?

And you can use LaTeX to do fractions... https://www.physicsforums.com/help/latexhelp/

 

[IDK10]

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.

 

[berkeman]

b = brightness (W m-2)

So how does the brightness fall off with distance, and why?

 

[IDK10]

So how does the brightness fall off with distance, and why?

What do you mean by fall off with distance?

 

[berkeman]

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)...

 

[IDK10]

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.

 

[Drakkith]

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.