How does Radiance change with a parabolic reflector?

In summary, the coil with no reflector has a radiant intensity of 2 W/sr, while adding a 10 sqcm reflector results in a radiant intensity of 20 W/sr. Adding a 100 sqcm reflector results in a radiant intensity of 200 W/sr. Finally, adding a very narrow beam will generate a radiant intensity of 1000 W/sr.
  • #1
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Lets say I have a coil that is 1cmx1cm in area that gets heat up. I am told that I get 2W/cm^2/sr output. So if I had 100 of them in an array, the total radiant intensity would be (2W/cm^2/sr x 100 x 1 sqcm =) 200W/sr.

Now, let's say I add a parabolic reflector around each coil. How would I estimate the increase in radiance and radiant intensity (in the direction of the reflector? Do I now use the aperture area of each reflector instead of the area of the coil? Do I multiply by 2pi since now I can able to see the radiance from the back of the coil? This is where I am getting confused.
 
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  • #2
The intensity(watts/sr) ## I=L*A ## where ## L ## is the radiance and ## A ## is the area of the source or reflector (i.e. illuminated/projected area) assuming 100% reflector reflectivity. The total power ## P ## will be the same (approximately) with reflector as without the reflector. The bare source will have a solid angle of as much as ## 4\pi ## steradians depending upon the intensity pattern that it has. (If it is spherical, it would radiate equally in all directions). The parabolic reflector will have a greatly reduced effective solid angle of beam coverage. Ideally (with 100% reflectivity and no light returning to the source from the reflector), power ## P=I*\Omega ## (where ## \Omega ## is the effective solid angle of the radiated pattern) will be the same for the bare source as for the source plus reflector. The radiance ## L ## is a constant in all of these calculations, so that in the case of conserved power ## P ##, one has ## A_1 * \Omega_1=A_2 * \Omega_2 ## where the subscript "1" is the bare source and subscript "2" is the source plus reflector. The parabolic reflector will make a narrow pattern( effective solid angle ## \Omega_2 ##), but the intensity normally would not be constant throughout the region of illumination. The last equation allows you to get a quick estimate of the size of the beam pattern (in steradians) that a reflector will provide. One can also write ## I_1*\Omega_1=I_2*\Omega_2 ## as a useful equation to see the tradeoff between intensity that the reflector generates versus the size of the beam pattern (solid angle). A larger reflector will give a higher intensity, but will necessarily generate a narrower beam.
 
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  • #3
So if I understand correctly, the area represents the projected aperture area?
So in my example, I said I have a coil that is 1cmx1cm in area. The coil radiates 2 W/cm^2/sr. Let's assume spherically.
With no reflector, the radiant intensity would be 2 W/sr?
If I have a 10 sqcm (100% reflective) reflector, the radiant intensity would be 20 W/sr?
If I have a 100 sqcm (100% reflective) reflector, the radiant intensity would be 200 W/sr?

Now how would I compare this with a very narrow beam, like from a laser? That is usually given in W. I am usually given an approx beam pattern where I can estimate the divergence angle. Based on that I can estimate a solid angle. However then the radiant intensity is an extremely high number since the angle is so small.
 

1. How does the shape of a parabolic reflector affect the radiance of light?

The shape of a parabolic reflector plays a crucial role in focusing and directing light, which ultimately affects the radiance. The parabolic shape allows for parallel light rays to be reflected towards a single focal point, resulting in a concentrated beam of light with high radiance. This is known as the "parabolic reflector effect."

2. Does the size of a parabolic reflector impact the radiance of light?

Yes, the size of the parabolic reflector can impact the radiance of light. A larger parabolic reflector will have a larger focal point, resulting in a wider beam of light with lower radiance. Conversely, a smaller parabolic reflector will have a smaller focal point, resulting in a more concentrated beam of light with higher radiance.

3. How does the material of a parabolic reflector affect the radiance of light?

The material of a parabolic reflector can affect the radiance of light in several ways. First, the reflectivity of the material impacts how much light is reflected, and therefore the intensity of the radiance. Second, the smoothness of the material's surface can affect how efficiently light is reflected, thus influencing the radiance. Finally, the material's ability to withstand high temperatures can impact the overall performance of the parabolic reflector and, consequently, the radiance of light.

4. What factors besides the parabolic shape can impact the radiance of light from a reflector?

Aside from the parabolic shape, other factors that can impact the radiance of light from a reflector include the angle of incidence of the light, the distance between the light source and the reflector, and the quality and cleanliness of the reflector's surface. Additionally, the type of light source and its characteristics, such as color and intensity, can also affect the radiance of light.

5. How does the distance between the light source and the parabolic reflector affect the radiance of light?

The distance between the light source and the parabolic reflector can impact the radiance in two ways. First, the closer the light source is to the reflector, the more focused the beam of light will be, resulting in higher radiance. Second, the angle of incidence of the light can change as the distance between the light source and the reflector changes, which can also affect the radiance. Generally, a shorter distance between the light source and the reflector will result in higher radiance.

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