If the mirror can be moved horizontally to the left or right, what is the greatest possible distance d from the mirror to the point where the reflected rays meet?

the distance d will be greatest when the rays are incident. the reflected area and the diameter of the mirror from an isolated triangle. the distance d bisects the triangle forming two right angle triangle. where d is 1 leg, d/2 is another leg, the reflected ray from the mirror to the point of intersection is the hypotenuse

tan Q = Y / X

So, the distance d from the mirror to the point that the rays intersect is always equal to the distance between the mirror and the point that the incident rays should intersect.

Independent variable is something that is changed in a experiment.