Why is radiance defined per projected area normal to the beam direction?

In summary, radiance is a measure of radiant flux per solid angle per projected area normal to the beam direction. It is necessary to project the surface segment normal to the beam in order to avoid the dependence of radiance on the definition and orientation of the area. Without this projection, the radiance would vary depending on the direction, making it a property of the interaction of light with a specific surface orientation rather than a property of the light itself. Additionally, radiance is commonly used as a measure of brightness, further supporting the idea that it is a property of the light itself.
  • #1
brightlint
3
0
Radiance is defined as radiant flux per solid angle per projected area normal to the beam direction: ##L = \frac{d^2 \Phi}{d \vec\omega \cdot d A_\perp}## where ##A_\perp = A \cos \theta## and ##\theta## is the angle between the beam direction ##\vec\omega## and the surface normal. I kind of understand that radiance is simply the infinitesimal flux ##d\Phi## contained in the infinitesimal cone/ray which is described by the infinitesimal solid angle and the surface segment ##d A##. However I don't understand why it's necessary to project the surface segment normal to the beam. Why would ##L = \frac{d^2 \Phi}{d \vec\omega \cdot d A}## be a bad definition of radiance?
 
Physics news on Phys.org
  • #2
Then L would depend on the definition of your area and its orientation relative to the flux. The number alone would become meaningless.
 
  • #3
mfb said:
Then L would depend on the definition of your area and its orientation relative to the flux. The number alone would become meaningless.

I'm still having trouble to see why that would be a problem. I would be glad if you or someone else could illustrate it with an example like this:

Suppose there is a surface segment ##d A## inside a sphere and the sphere emits light on the inside like a Lambertian radiator. If I measure the incident radiance at the surface segment ##d A## coming from a certain direction ##d \vec\omega## without the projection of ##dA## normal to the beam, then the measured value would be small for directions near the horizon because of the Tilting principle. However, if I project the surface segment normal to the beam, then the radiance would be constant across the whole hemisphere.

Is this correct so far? Why would it be meaningless if the radiance would change depending on the direction?
 
  • #4
brightlint said:
Why would it be meaningless if the radiance would change depending on the direction?
Radiance is supposed to be a property of the light, not a property of the interaction of light with some (not necessarily real!) surface with some specific orientation.
 
  • #5
Why don’t we use a differential area normal to the beam in the first place, instead of projecting a non-normal one?

Besides that, radiance is often described as an measure for how bright an object appears, wouldn't that be a property of the interaction of light with a surface?
 

1. Why is radiance defined per projected area normal to the beam direction?

Radiance is defined per projected area normal to the beam direction because it is a measure of the amount of energy emitted per unit area in a specific direction. By normalizing the value to the projected area, it allows for a more accurate comparison of radiance values between different surfaces and at different angles.

2. What is the significance of defining radiance per projected area normal to the beam direction?

The significance of defining radiance per projected area normal to the beam direction is that it takes into account the variation in surface area that is projected in the direction of the beam. This allows for a more precise measurement of the amount of energy being emitted in a specific direction.

3. How is radiance per projected area normal to the beam direction calculated?

Radiance per projected area normal to the beam direction is calculated by dividing the radiance value by the projected area of the surface in the direction of the beam. This value is then expressed in units of watts per square meter per steradian (W/m2/sr).

4. What is the difference between radiance and irradiance?

Radiance and irradiance are both measures of energy, but they differ in the direction in which the energy is measured. Radiance is a measure of energy emitted in a specific direction per unit projected area, while irradiance is a measure of energy received by a surface per unit area.

5. How does radiance per projected area normal to the beam direction relate to the intensity of a light source?

Radiance per projected area normal to the beam direction and intensity are both measures of the amount of energy emitted in a specific direction. However, intensity is a measure of the total energy emitted by a light source, while radiance per projected area normal to the beam direction takes into account the surface area of the object emitting the light in the direction of the beam.

Similar threads

Replies
17
Views
3K
  • Other Physics Topics
Replies
7
Views
9K
  • Other Physics Topics
Replies
13
Views
5K
  • Other Physics Topics
Replies
2
Views
3K
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
942
Replies
2
Views
18K
  • Introductory Physics Homework Help
Replies
7
Views
768
  • Advanced Physics Homework Help
Replies
3
Views
957
  • Advanced Physics Homework Help
Replies
6
Views
2K
Back
Top