A dentist uses a small concave mirror of radius of curvature magnitude 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 mirror of radius of curvature magnitude 4.0cm to inspect a tooth held 1.0cm in front of the mirror. Under the sign convention CV1 used in this book (light travels left to right; so>0 for a real object to the left; R>0 when the centre of curvature lies to the right of the vertex), a student writes the following solution. "The mirror is concave, so I take R=+4.0cm. Then f=−R/2=−2.0cm. Using 1/so+1/si=1/f with so=1.0cm: 1/si=1/f−1/so=−1/2.0−1/1.0=−1.5cm−1, so si=−0.67cm. The magnification is MT=−si/so=+0.67, so the tooth appears virtual, upright and slightly reduced."
((a)) Identify the error in the student's reasoning and explain, from CV1, what the correct sign of R should be.
((b)) Redo the calculation correctly to find the image distance si and the transverse magnification MT, and state whether the image is real or virtual, upright or inverted, and enlarged or reduced.