The first and most basic concept of light you should know is:
Direct light vs Diffuse or soft light. You probably already know it on source lights, I will describe it because is the same concept.
You have a spot light, where the beam source is a tiny spot (a) and cast a hard shadow (b).
When you have a bigger sized source light it becomes a diffused one. The beams from the point (c) go in a diferent direction and cast a shadow in another point (d)
Of course, there are not just 2 points of light, but an infinite array of little light sources, which, combined gives a soft shadow (e), where the darker zone is defided by (b) and the lightest zone by (d) in the previous diagrams.
- In real life, this light either it is absorbed or bounces. The angle on a reflective surface (mirror) of this reflected ray (g) is the same opposite angle as the incident one (f).
Some rays simply go away from your object and do not come back (h).
- But in a diffuse material, a matt material, these rays do not bounce at that angle alone, they explode, they scatter (i) and those that on a reflective surface would not hit the object anymore, come back and lit a bit the object (j).
- One important thing to understand, is that normal light scatter, this is, are not parallel rays, they come from a point to different directions, If you are close, you get more concentrated rays (k), so the further away you are from this little point, the fewer (l) rays hit the zone.
- One additional concept is the angle of difusion. This is the concept that light will less likely to bounce at some angles. More rays will bounce at some angles similar to the incident angle (m) than an angle too far from this "ideal" angle (n).
- On a very, very rough material, the little bumps on it, bounce more light back (o) than further away, they are like little walls. An example of this material could be a carpet.
- The main light law here to understand how distance afects the ilumination is the inverse square law, that states that the further away you are from the light source the less light you get in a square inverse proportion.
The answers to your questions on the attached image.
A. Shouldn't a and b on the right be the same value since they are being hit at the same angle? yet, both in Blender and in real life they are not the same value.
No, they are not hit at the same angle because the material you are using is not a mirror, it is a matt material, exactly like a pool table. See point 6.
B. What am I missing here?
What you are missing is that the further away from the source light you are the less light you get, this is the inverse square law.
C. Is the angle at which the light hits the object the only thing that determines its value?
How the light hit an object is determined by
Angle of the incident light on the reflective material
Material, color, and roughness (glossy vs matt and all the in between values).
Distance from the source light. This is specially true on a matt material, this matt material (the floor) is a new light source now.
D. Does this mean there are more rays hitting B and there are A?
E. How do I determine how many rays are hitting an area?
By the inverse square law. The closer you are to this (new) source light (the matt material) more light you have, the further away less light you get.
But you need to determine two light sources, the incident light and the bounced light. In this case the inverse square law applies more to the bounced light, as this is the main problem you are describing.
F. And how does the cast shadow get lit back up, where are those bounces corning from?
You are mixing concepts.
The cast shadow in your diagram is gray, this is implying that there is an ambient light that you are not seeing, the roof of a room, the sky of the planet.
But on your diagram what you consider cast shadow is self shadow, that, it is also gray because the ambiet ligh, but have some bounced green light from all over the floor.
In the image you are posting, the "only the bounced light" render, there is a chance you are "forcing" the Blender material too much making it not natural.
I am simulating roughly this bounced light.
See the angles depending on the type of the floor's material. Your example has more light on the right, but it looks more like if this reflective surface is in an angle.