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?
1/f = 1/d​o​ + 1/d​ m = h​i/​ h​o​ = -d​i/​ d​o

Answer 1

$$m=\frac{h_i}{h_o}=-\frac{d_i}{d_o}\\\frac{8.5}{19}=-\frac{d_i}{36.4}\to d_i=-16.3\ cm$$

$$\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}\\\frac{1}{f}=\frac{1}{36.4}+\frac{1}{-16.3}\\f=-29.5\ cm$$