As in the image we can see that ray of light is bouncing off objects. Black ones are opaque objects and white ones are transparent objects. I want to calculate how many times a ray of light bounces to reach a particular point, "without tracing rays". I am looking for the mathematical equation(that takes scene and a point as its input and outputs the number of bounces) that tells how many times ray of light will bounce to reach a particular point.
Is this type of mathematical equation exists? If not, which area of mathematics should I study to find solution to this problem?