# Radiance change with light distance

• Gadersd
In summary, the conversation discusses the use of Monte Carlo integration to solve the rendering equation and the concept of radiance not changing with distance. The reference mentioned confirms that light energy associated with a ray will stay with that ray, but it doesn't mean that a point light source can illuminate objects from an infinite distance away. The conversation also touches on the limitations of the model, including the increase in computational cost and the accuracy of measuring curvature.

#### Gadersd

I am trying to solve the rendering equation with monte carlo integration. I gather all of the incoming radiance from light sources and plug it into the rendering equation. A reference I am using said that radiance does not change with distance. Does this mean that a point light source will illuminate objects from a infinite distance away since the radiance does not change?

Not sure. Can you provide a link to your reference?

I can't be sure, but it appears to say that whatever quantity of light you have associated with a ray will stay with that ray. I wouldn't say that a point source can illuminate an object an infinite distance away, since light is not physically composed of rays.

In this modelling scenario you are modelling the path of individual rays which may as well be regarded as individual photons for the purpose of intuition, although the amount of energy associated with each ray is likely to be much greater than an actual photon.

Yes the ray will travel infinitely if running the simulation does not introduce an interaction with another object. But what probability is associated with this outcome in your scenario?

The model appears limited by the quantity of light that can be associated with a ray, and also by the physical accuracy of modelling reflections between ideal flat surfaces separated by large distances.

The first limitation is due to the increase in computational cost of tracing more rays, each having less energy associated with it (as ray energy approaches photon energy resolution is improved). The second limitation is due to measuring and encoding accurate curvature.

The first limitation is obvious and tangible. The second is barely of concern for basically all pracital applications.

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## 1. How does the radiance of light change with distance?

As light travels through space, its radiance decreases with distance. This is due to the inverse square law, which states that the intensity of light is inversely proportional to the square of the distance from the source. In simpler terms, as the distance from the light source increases, the amount of light that reaches a given area decreases.

## 2. What factors affect the change in radiance with distance?

The change in radiance with distance is affected by several factors, including the intensity of the light source, the size and shape of the light source, and the medium through which the light is traveling. These factors can alter the amount of light that reaches a given area, resulting in a change in radiance.

## 3. How does the change in radiance with distance impact the perception of brightness?

The change in radiance with distance can significantly impact the perception of brightness. As the distance from the light source increases, the amount of light that reaches our eyes decreases, causing the perceived brightness to decrease as well. This is why objects appear dimmer when they are farther away from a light source.

## 4. Can the change in radiance with distance be calculated?

Yes, the change in radiance with distance can be calculated using the inverse square law. This involves measuring the distance from the light source and the intensity of the light at that distance, and then using the formula to determine the change in radiance. However, the calculation may become more complex when other factors, such as the medium through which the light is traveling, are considered.

## 5. How does the change in radiance with distance impact the energy of light?

The change in radiance with distance does not impact the energy of light itself. The energy of light remains constant, but the amount of energy that reaches a given area decreases as the distance from the light source increases. This is because the same amount of energy is spread out over a larger area, resulting in a decrease in intensity or radiance.