In order to find the position of the image, we can use the formula below:
[tex]\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}[/tex]Where f is the focal length, do is the object distance and di is the image distance.
So, using f = -0.2 meters and do = 0.50 meters, we have:
[tex]\begin{gathered} \frac{1}{-0.2}=\frac{1}{0.5}+\frac{1}{d_i}\\ \\ -5=2+\frac{1}{d_i}\\ \\ \frac{1}{d_i}=-7\\ \\ d_i=-\frac{1}{7}=-0.1429\text{ m} \end{gathered}[/tex]Therefore the image is located at -14.29 cm from the mirror.
Now, to calculate the size of the image, we can use the formula below:
[tex]\begin{gathered} \frac{-d_i}{d_o}=\frac{h_i}{h_o}\\ \\ \frac{-(-0.1429)}{0.50}=\frac{h_i}{0.25}\\ \\ 0.1429=2h_i\\ \\ h_i=0.07145\text{ m}=7.145\text{ cm} \end{gathered}[/tex]Therefore the image size is 7.145 cm.
