In: Physics
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
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