How to understand the steradians equation for measuring a sphere of light?

In summary, Lumens and Candelas are measured within a given space. If a source is isotropic, meaning equally bright in all directions, then the number of candela will just be equal to the total number of lumens divided by 4pi steradians, which is the total solid angle of the entire sphere (all directions into which the source is emitting the light).
  • #1
squeekymouse
4
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TL;DR Summary
I am trying to understand the steradians equation for measuring a sphere of light.
Hello and please know I am very greatful for your help!
I am wanting to learn how to measure light. I have chosen a specific light for this to help me better understand.
Lm- 7800
CD-620.7
So, I got that far, lol. I don't really know how to input the numbers for the Steradians equation, I have an idea, but I would like to see how it is solved so I can understand it better.
1(cd) • 4 pi (sr) = 4 pi (cd•sr) = 12.57 (lm)
Thank you again for helping me learn 😁
 
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  • #2
Can you explain what Lm and CD are? It would help if you had units attached to the numbers. Also, what is the steradians equation that you are referring to? A steradian is a unit of solid angle so it is not clear what you are asking about.
 
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  • #3
kuruman said:
Can you explain what Lm and CD are? It would help if you had units attached to the numbers. Also, what is the steradians equation that you are referring to? A steradian is a unit of solid angle so it is not clear what you are asking about.
I apologize, I am trying to understand how Lumens and Candelas are measured within a given space.
 
  • #4
Let me try this another way. If it is an 8'x 8'x 8' room and I wanted 60 foot candles of light and I know that it will equal 4800 lumen. What would that equation look like? I can use an internet calculator for the information, but I am interested in seeing the actual equation, so I can change the size of the room or foot candles as needed.
 
  • #5
squeekymouse said:
Let me try this another way. If it is an 8'x 8'x 8' room and I wanted 60 foot candles of light and I know that it will equal 4800 lumen. What would that equation look like? I can use an internet calculator for the information, but I am interested in seeing the actual equation, so I can change the size of the room or foot candles as needed.
For your problem, it seems that candela (lumens per unit of solid angle) are largely irrelevant to your problem. If a source is isotropic, meaning equally bright in all directions, then the number of candela will just be equal to the total number of lumens divided by 4pi steradians, which is the total solid angle of the entire sphere (all directions into which the source is emitting the light).

You want to know something different, which is the brightness or illumination (in lumens per unit area) at a certain viewing distance from the source. You are using foot-candles (lumens per ft2), but in the future I would strongly encourage you to use lux (lumens per m2) instead, because US/Imperial units are a pain.

Anyway, you've stated that you know for sure that the source emits a total output of 4800 lumens into the room. The question is what area that output will be spread out over at a given distance. Again, we'll assume that the source is isotropic (emits the same in all directions) so that we can just divide. (Otherwise you are dealing with differentials i.e. calculus). At the very edge of the room, the total output is spread out over a sphere of radius 8 ft. This sphere has total surface area 4*pi*(8 ft^2), which works out to about 804 ft^2. The number of foot-candles at the edge of the room will just then be

(total output in lumens)/(total surface area) = (4800 lm)/(804 ft^2) = 5.9 lm/ft^2

Or in other words, just under 6 foot-candles of illumination at the very edge of the room. If you need more, you need to either get closer to the light source or increase its total output (in lumens). I hope that helps.
 
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  • #6
LastScattered1090 said:
For your problem, it seems that candela (lumens per unit of solid angle) are largely irrelevant to your problem. If a source is isotropic, meaning equally bright in all directions, then the number of candela will just be equal to the total number of lumens divided by 4pi steradians, which is the total solid angle of the entire sphere (all directions into which the source is emitting the light).

You want to know something different, which is the brightness or illumination (in lumens per unit area) at a certain viewing distance from the source. You are using foot-candles (lumens per ft2), but in the future I would strongly encourage you to use lux (lumens per m2) instead, because US/Imperial units are a pain.

Anyway, you've stated that you know for sure that the source emits a total output of 4800 lumens into the room. The question is what area that output will be spread out over at a given distance. Again, we'll assume that the source is isotropic (emits the same in all directions) so that we can just divide. (Otherwise you are dealing with differentials i.e. calculus). At the very edge of the room, the total output is spread out over a sphere of radius 8 ft. This sphere has total surface area 4*pi*(8 ft^2), which works out to about 804 ft^2. The number of foot-candles at the edge of the room will just then be

(total output in lumens)/(total surface area) = (4800 lm)/(804 ft^2) = 5.9 lm/ft^2

Or in other words, just under 6 foot-candles of illumination at the very edge of the room. If you need more, you need to either get closer to the light source or increase its total output (in lumens). I hope that helps.
Thank you so much for taking the time to explain this to me Especially with me not being very clear about what I am asking. You're awesome!
 
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  • #7
squeekymouse said:
Thank you so much for taking the time to explain this to me Especially with me not being very clear about what I am asking. You're awesome!
No problem, glad to be of help! :)
 
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1. What is the steradians equation?

The steradians equation is a mathematical formula used to measure the solid angle of a sphere of light. It is represented by Ω = A/r², where Ω is the solid angle, A is the area of the sphere, and r is the radius of the sphere.

2. How is the steradians equation used to measure a sphere of light?

The steradians equation is used to calculate the solid angle of a sphere of light, which represents the portion of the sphere's surface that is visible from a specific point. This measurement is important in understanding the intensity and distribution of light from a source.

3. What is the relationship between steradians and radians?

Steradians and radians are both units of measurement for angles. One steradian is equal to the solid angle subtended by a spherical surface at the center of the sphere, which is equivalent to the area of a sphere's surface divided by the square of its radius. One radian is equal to the angle subtended by an arc of a circle with the same length as the circle's radius. Therefore, one steradian is equal to approximately 3282.8 square radians.

4. Can the steradians equation be used for non-spherical light sources?

Yes, the steradians equation can be used for any light source that has a defined surface area and can be approximated as a sphere. This includes non-spherical sources such as cones, cylinders, and pyramids.

5. How does the steradians equation relate to the inverse square law?

The steradians equation is closely related to the inverse square law, which states that the intensity of light decreases in proportion to the square of the distance from the source. The steradians equation takes into account the distance from the source (represented by r²) when calculating the solid angle, which is an important factor in understanding the intensity of light at a given point.

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