Light and optics: A mirror in an operating room

Operating rooms use bright overhead lights to increase visibility during surgical procedures. The operating room light shown below uses a high power light bulb surrounded by a curved parabolic concave mirror. The light bulb is placed at the focal point of the curved parabolic mirror. The dashed line represents the principal axis of the curved mirror. The point C represents the center of curvature of the curved mirror. The back of the mirror is also metallic, shiny, and reflective.

Figure 1. A diagram of an operating room, including the presence of a light bulb and a mirror.

During one surgery, the following scenarios occur:

Scenario 1: While waiting for her procedure to start, a patient whose face is located near point D is looking up at the mirror along the principal axis. The operating light is not turned on, but the room is bright enough for her to see a reflection of her face in the mirror.

Scenario 2: the patient starts to sit up, causing her face to move along the principal axis from point D to point C.

Scenario 3: Before the operation, the surgeon is looking at his reflection in the back of the curved mirror. The surgeon’s face is located near point A.

Scenario 4: The light bulb was moved from its initial location and placed very, very far away from the mirror along the principal axis, so that the light rays are essentially parallel when they reach the curved mirror.