I am currently studying the basics of photometry to better understand the rendering equation of Kajiya. One thing I'm currently struggling with is Lambert's cosine law.
Let's go over the premises:
- A lambertian surface scatters light evenly in all directions.
- The projected surface area decreases with the cosine of the viewing angle.
For the luminous intensity from a viewing angle $I_\theta$ I have the following equation: $$I_\theta = I_0 \cdot cos(\theta).$$ My question is: why should the luminous intensity be decreasing with the angle if I can still see the whole surface? If the light is scattering evenly in every direction, as was the premise for a lambertian surface, why should the projected surface area matter at all. Shouldn't I still recieve the same amount of light, but only in a more concentrated beam?
Thank's in advance to anyone who can help me get out of my confision, which I've been stuck in for the whole last week.