Question

Who "discovered" the sign conventions for spherical mirrors?

Answer 1

See the beauty of science lies in the fact that there are no conventions to be followed.

Yes, your heard right.

How come light know that we are following Cartesian Coordinates or Polar coordinates?

See, this all is relative, we can define our new sign convention and the formulae would be same. Provided you start from scratch and derive everything again. Believe me, it works the same way round.

Units, conventions all are just relative. These are made just that all scientists in the world follow a same league and no one gets confused.