how a golf scope works , whats physics laws it operate on what is accuracy in which it can measure distance?

Answer 1

The ones I have seen just use a simple geometric (or trigonometric) principle based on triangulation.
The height of the flag locating the hole is standardized.
Therefore, from where you are standing, the greater the distance to the flag, the shorter the leg of the triangle formed by the flag staff is. Basically, you form an acute triangle where two legs are of essentially identical length. Those two legs, if drawn on paper, would be the two legs from the scope (your location) to the top and the bottom of the flag staff.
The third leg of the triangle is the flag staf itself.
The scope measures the angle formed . Since the length of the leg formed by the flag staf is known, and the angle is known, then the length of each of the other two legs can be accurately calculated. That length is your distance to the hole.
The scope reads out, not in degrees of angle, but in distance.