I know that aperture and DOF are inversely proportional. But, can anybody explain to me the Physics/Optics behind that? What's the mathematical relation that relates aperture with DOF?
You aren't going to be able to learn these equations and do them in your head to map an ƒ number to a depth of field in, say, feet. This is why there are so many DoF calculators floating around. I wrote one of many.