Question

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?

Answer 1

Reflected rays from an object in front of a flat mirror appear to converge at a point behind the mirror that is equal to the object distance from the mirror; in this case, 2 meters, forming a virtual image.

Step-by-step explanation:

The question related to how reflected rays from an object in front of a flat mirror converge to form an image involves understanding the law of reflection. According to this law, the angle of incidence equals the angle of reflection, meaning that reflected rays will appear to converge at a point behind the mirror at the same distance the object is in front of it. Therefore, for an object 2 meters in front of a mirror, the reflected rays will seem to converge 2 meters behind the mirror, creating a virtual image of the object.

This phenomenon can be explained further by discussing the properties of images formed by flat mirrors. A flat mirror has an infinite focal length, so the image distance (di) is equal to the magnitude of the object distance (do) but considered negative since the image is virtual. If ray 1 is normal to the mirror and ray 2 is at a 5° angle, after reflection, both will still appear to come from the same point behind the mirror, at a distance equal to the object distance in front of the mirror (2 meters).

Answer 2

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.