Question

A 19.0 cm tall figurine is placed 36.4 cm in front of a concave mirror. An image is found to be - 8.5 cm tall. What is the focal length of the mirror?

Answer 1

Let's first find the image distance from the magnification equation:

$$M=\dfrac{h_i}{h_o}=-\dfrac{d_i}{d_o},$$ $$d_i=-\dfrac{d_oh_i}{h_o}=-\dfrac{36.4\ cm\cdot (-8.5\ cm)}{19.0\ cm}=16.3\ cm.$$

Finally, we can find the focal length of the mirror from the mirror equation:

$$\dfrac{1}{d_o}+\dfrac{1}{d_i}=\dfrac{1}{f},$$ $$f=\dfrac{1}{\dfrac{1}{d_o}+\dfrac{1}{d_i}},$$ $$f=\dfrac{1}{\dfrac{1}{36.4\ cm}+\dfrac{1}{16.3\ cm}}=11.26\ cm.$$

Answer:

$f=11.26\ cm.$