Lambertian Surface: Exploring Radiant Intensity and Incident Angles

[JunYoung]

Hello. I'm curious about the lambertian surface. Suppose in a given flat, surface of area A the light comes in, the incident angle being theta. The observer vector coincides with the light source, the angle between the normal of the surface being theta also.

Then, when I calculate the radiant intensity, [w/sr^-1] should it be proportional to cos(theta)^2 or cos(theta)? Thanks.

 

[AndyW]

Hello there,

Thank you for your interest in lambertian surfaces. To answer your question, the radiant intensity of a lambertian surface is proportional to cos(theta). This is because a lambertian surface is a perfectly diffuse reflector, meaning that it reflects light equally in all directions. In other words, the amount of light reflected is independent of the incident angle.

To understand this better, let's consider a simple example. Imagine a perfectly white, lambertian surface facing a light source directly. The incident angle and the angle between the normal of the surface would both be zero. In this case, the surface would reflect all of the light it receives, resulting in a radiant intensity of 1.

Now, if we change the incident angle to 45 degrees, the reflected intensity would still be 1, even though the angle between the normal and the light source has increased. This is because the lambertian surface reflects light equally in all directions, regardless of the incident angle.

In summary, the radiant intensity of a lambertian surface is proportional to cos(theta), not cos(theta)^2. I hope this helps clarify your understanding of lambertian surfaces. Let me know if you have any further questions.