A dentist uses a small concave (converging) mirror of focal length to inspect a…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Geometrical optics and imaging

Optics and Photonics, Ch Image formation by mirrors and lenses

Problem

A dentist uses a small concave (converging) mirror of focal length

f = 25\ \text{cm}

to inspect a patient's tooth. The tooth sits

s_o = 10\ \text{cm}

from the mirror, on the axis. Use the sign convention of this chapter: light travels left to right,

s_o > 0

for a real object,

s_i > 0

for a real image in front of the mirror (to the left, back towards the object), and

f = -R/2

with

f > 0

for this converging mirror. A colleague wants to photograph the magnified image the dentist sees. She sets up a camera whose lens is

50\ \text{cm}

in front of the mirror (on the same side as the tooth), pointed at the mirror. ((a)) Find

s_i

and state whether the image is real or virtual. ((b)) The colleague argues: "the image isn't really there, so however the camera is focused it will only ever record the mirror's surface in sharp focus, at

50\ \text{cm}

." Say whether this is correct, and find the actual distance from the camera lens at which the camera must be focused to record the image sharply.

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