Final answer:
For ceilings over 114 inches, fixture height will vary based on the room's function and fixture type. Fixtures using concave mirrors need to consider the mirror's focal length and the desired projection on the floor. For accurate fixture placement, both optical physics and electrical considerations must be taken into account.
Step-by-step explanation:
The height at which to hang fixtures for ceiling heights greater than 114 inches (9 feet 6 inches) can depend on several factors, including the function of the room, the type of fixtures, and aesthetic considerations. However, if the fixtures involve concave mirrors, as suggested by the reference to projecting on the bathroom floor and reaching a height of 3.0 meters, this implies that there is an aspect of optical physics involved. The use of concave mirrors behind the filaments in ceiling fixtures is typically intended to focus the light, potentially for tasks such as makeup application or shaving in a bathroom context.
To determine the exact height for such fixtures in a room with a high ceiling, one needs to consider the focal length of the concave mirrors and the desired size and shape of the light projected on the floor. It is also important to factor in the electrical components, which you may need to consult with a qualified electrician or instructor for the appropriate level of complexity. Generally, for functional lighting, fixtures are hung lower to ensure adequate light reaches the area where it's needed, whereas for ambient lighting, they may be hung higher.