The illumination lights in an operating room use a concave mirror to focus an image of a bright lamp onto the surgical site. One such light has a mirror with a focal length of \(15.0 \mathrm{~cm}\). Use ray tracing to find the position of its lamp when the patient is positioned \(1.0 \mathrm{~m}\) from the mirror (you'll need a careful drawing to get a good answer).