# Can ambient light reflection of a surface be larger than diffuse reflection?

According to Phong's reflection model, there are different reflection constants (k) and different intensities of the light source (i) for ambient, diffuse, and specular terms:

$$I_p=k_ai_a+\sum_{m \in lights} \left(k_d(\hat{L}_m \cdot \hat{N})i_{m,d} + k_s(\hat{R}_m \cdot \hat{V})^\alpha i_{m,s} \right)$$

1. When a pixel is under shadow (umbra), does the equation become this way: $$I_p=k_ai_a$$ ?

2. Suppose we only have one major light source. So the equation can be something like this: $$I_p \approx k_ai_a+ k_d(\hat{L} \cdot \hat{N})i_{d} + k_s(\hat{R} \cdot \hat{V})^\alpha i_{s}$$

Can the ambient portion of pixels ($$k_ai_a$$) become larger than the rest (even with no specular reflection)?

Basically, can this happen: $$k_ai_a \stackrel{?}{\geq} k_d(\hat{L} \cdot \hat{N})i_{d}$$

3. Is there any relationship between $$k_a, k_d, k_s$$ and $$i_a, i_d, i_s$$ of one point in a scene?

• There's no relationship between those. The ambient term is a heuristic anyways that's there to substitute for the lack of indirect illumination - not that it does a good job at that. Nov 5, 2020 at 17:58
• @lightxbulb so for example on a sunny day outdoors, can the skylight (ambient) be larger than sunlight (diffuse)? I feel like there should be some kind of relationship between diffuse and ambient reflection when there is only one light source in a scene. Nov 6, 2020 at 13:06
• There is actually no such thing as the ambient term. It's an outdated model and is just an approximation. When you get into pathtracing this ambient term gets replaced by indirect illumination which is again based on either diffuse or specular terms or any other term depending on the BRDF of the surface. Nov 6, 2020 at 17:54
• Microfacet models are used commonly. More complex materials require a layered approach. As for the other question, the answer is not neccessarily. Think of a scenario where an object is lit by sun directly and it's again lit by placing a mirror or a magnifying glass at a specific angle so all the light converges or reflects in the same direction and arrives at our said object. This way light coming indirectly either by refraction through the glass or reflection illuminates the object more and creates a blinding whiteness. Reason why u see caustics. Nov 7, 2020 at 6:12
• Phongs reflection model is a pure guess it makes nontrue assumptions. But its simple, by design, so thats why it gets used. Nov 9, 2020 at 7:19