In a modern communal bathing facility designed with an emphasis on privacy and comfort, there are a series of partitioned stalls arranged in a semi-circular fashion around a central washing area. Each stall is separated by high partitions that do not reach the ceiling, allowing for air circulation, but are tall enough to prevent direct line of sight into adjacent stalls for an average-height individual standing upright on the floor of the stall. The open side of each stall faces away from the central area and towards the outer walls which are mirrored, ostensibly for personal grooming purposes.

On this particular day, the facility is moderately busy, with various patrons enjoying their time in the individual stalls. Kofi, who is notably taller than the average person, enters the bathing area and chooses a stall roughly at the midpoint of the semi-circle. Meanwhile, at the stall on the farthest end of the semi-circle, Rania, who is of average height, has been bathing but decides to stand on the small bench provided in her stall to reach for an item on the top shelf. She is now temporarily tall enough such that her eyes are just above the level of the partition.

Given the arrangement of stalls, the reflective surfaces, and the heights of the individuals involved, what can Kofi and Rania see regarding the other patrons within the bathing facility? Consider the reflections, the line of sight, and the geometry of the semi-circle. Discuss their perspectives.
To understand what Kofi and Rania can see, it is essential to consider the geometry of the room, the height of the partitions, the mirrors on the outer walls, and their relative positions.

Kofi, being taller than average, will have a direct line of sight over the partitions while standing on the floor of his centrally located stall. However, because the baths are arranged in a semi-circular fashion, his view of the stalls to his immediate left and right will be blocked by the partitions. He may, however, catch glimpses of more distant patrons reflected in the mirrors on the outer walls as they stand or move, because the angle of incidence is equal to the angle of reflection. If he specifically looks into the mirror, he may see parts of the reflections of people in stalls that are beyond his immediate neighbors, but not directly next to those stalls because the partitions' angles would obstruct those reflections.

Rania, when standing on the bench, similarly has an elevated line of sight that goes beyond the usual height the partitions are designed to conceal. She is positioned at the end of the semi-circle, giving her a different vantage point than Kofi. Due to the curvature of the semi-circle, Rania would not be able to see directly into the stalls on the opposite end because her line of sight is blocked by the partitions immediately next to hers. However, the mirrored walls at her end of the semi-circle will reflect parts of the opposite stalls. Depending on the precise angles, Rania could see reflections of individuals in stalls that are not adjacent to Kofi's stall but rather are located towards the opposite end of the semi-circle.

Both Kofi and Rania's ability to see other patrons will be limited and intermittent because the other individuals would need to be in positions where their bodies are reflected at angles that can be seen either directly or via the mirrored walls. Moreover, since the stalls are partitioned and the mirrors line the outer walls, only a limited range of angles would allow for sightlines that reveal other patrons, and these sightlines will largely contain fragmented images rather than a full view.

The reflections seen by Rania would be different from those seen by Kofi due to their locations. Since Rania is at the end of the semi-circle, she is in a position where the curvature of that arrangement would allow reflections from the opposite stalls to reach her, while Kofi's mid-point position would cause many reflected sightlines from opposite stalls to be obscured by the partitions closer to him in the semi-circle.