Question

A dentist uses a curved mirror to view the back side of teeth in the upper jaw. Suppose she wants an upright image with a magnification of 1.5 when the mirror is 1.9 cm from a tooth. Should she use a convex or a concave mirror? What focal length should it have?

Answer 1

She should use a concave mirror The reason is it can produce highly magnified images which is upright

Given magnification \(M=1.5\)

Object distance \(u=1.9 \mathrm{~cm}\)

\(M=-\frac{v}{u}\)

\(\Rightarrow v=-m u=-1.5 \times 1.9=-2.85 \mathrm{~cm}\)

From the mirror formula \(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\)

Substituting the values we get

\(\frac{1}{f}=\frac{1}{1.9}-\frac{1}{2.85}\)

\(\Rightarrow f=5.7 \mathrm{~cm}\)

Focal length of the mirror \(f=5.7 \mathrm{~cm}\)