Lambert's Cosine Law: Understanding Diffuse Reflection

[Ja4Coltrane]

Hello,
I have a quick question relating to Lambert's cosine law for diffuse reflection. My understanding of the law is that given an isotropically illuminated surface, the reflection distribution goes with the cosine of the zenith angle.

Now my question is whether or not that law holds for a single ray. That is, suppose a ray hits a surface at an arbitrary incident angle. Is the probability distribution for the direction of reflection lambert's law as well? Or does the law only hold on average for a large number of incident rays in random directions?

Thanks!

 

[Dr Lots-o'watts]

My understanding is that the law is a mathematical statement that represents an ideal. How we go about to make it happen to is up to us.

In the case of actual diffuse reflectors, the relation is more easily achieved by illuminating from everywhere. The closer the surface is to a perfect Lambertian reflector, the more you can allow yourself to have a single ray as source. In practice there is a specular component, however small it may be.

 

[sir-pinski]

Hello,
That's a great question! Lambert's cosine law does indeed hold for a single ray, but it is important to note that it is a statistical law and is most accurate when applied to a large number of incident rays. This is because the law is based on the assumption of isotropic illumination, meaning that the incident rays are coming from all directions. In reality, this is rarely the case and the law may not hold as accurately for a single ray. However, in most practical applications, the law is still a good approximation and can be used to predict the diffuse reflection of a single ray. I hope this helps clarify your understanding of Lambert's cosine law.