Question

A dentist uses a curved mirror to view the back side of teeth on the upper jaw. Suppose she wants an erect image with a magnification of 2.0 when the mirror is 1.2 cm from a tooth. (Treat this problem as though the object and image lie along a straight line.)

Part A
Use ray tracing to decide whether a concave or convex mirror is needed, and to estimate its focal length.
concave?
or
convex?


Part B
Use ray tracing to estimate its focal length.
Express your answer using two significant figures.
f = ___________cm

Answer 1

Magnification is \(\mathrm{M}=2.0\)

object distance is \(\mathrm{p}=1.2 \mathrm{~cm}\)

Magnification \(\mathrm{M}=-\mathrm{q} / \mathrm{p}\)

Here \(\mathrm{q}\) is image distance.

Image distance \(q=-M p\)

$$ \begin{array}{l} =-(2)(1.2 \mathrm{~cm}) \\ =-2.4 \mathrm{~cm} \end{array} $$

From mirror formula

$$ \begin{array}{l} 1 / f=1 / p+1 / q \\ =1 / 1.2+1 /-2.4 \\ \quad=0.416 \mathrm{~cm} \end{array} $$

Focal length \(f=2.4 \mathrm{~cm}\)

It is concave mirror