Geometrical Optics and Image Formation (4D) Practice Test

A handheld otoscope uses a concave mirror (thin spherical approximation) to concentrate light into a patient’s ear canal. The mirror has focal length $f = 5.0\ \text{cm}$. The filament of the lamp is placed $d_o = 15\ \text{cm}$ in front of the mirror along the principal axis. Based on the mirror equation, which outcome is most consistent with the described optics principle?

A surgical headlamp uses a converging lens to collimate light from an LED so the illuminated field is uniform at working distance. The LED is positioned on the optical axis at a distance equal to the lens focal length. The design team checks the beam by placing a screen several meters away. Using the thin-lens equation as the central concept, which outcome is most consistent with this setup?