Question

Santa checks himself for soot as he came off a chimney, using his reflection in a silvered Christmas tree ornament 0.750 m away. The diameter of the ornament is 7.20 cm. Standard reference texts state that he is a "right jolly old elf," so we estimate his height to be 1.60 m. a) Where and how tall is the image of Santa formed by the ornament? b) Is it erect or inverted?

Answer 1

This is a convex mirror with a focal length of -3.6 cm. Where the image is formed can be found with the mirror equation:

$$-\frac{2}{R}=\frac{1}{o}+\frac{1}{i},\\\space\\ i=-\frac{Ro}{2o+R}=-\frac{7.2\cdot75}{2\cdot75+7.2}=-3.4\text{ cm}.$$

The magnification is

$$M=-\frac{i}{o}=-\frac{-3.4}{75}=0.045,$$

the image will be

$$h_i=Mh_o=0.045\cdot160=7.3\text{ cm}$$

tall. It is erect.