In order to calculate the object's position, 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's position and di is the image's position.
Using f = 0.5 m and di = -0.19 m (we use a negative value because the image is virtual), we have:
[tex]\begin{gathered} \frac{1}{0.5}=\frac{1}{d_o}+\frac{1}{-0.19}\\ \\ 2=\frac{1}{d_o}-5.263\\ \\ \frac{1}{d_o}=2+5.263\\ \\ \frac{1}{d_o}=7.263\\ \\ d_o=\frac{1}{7.263}\\ \\ d_o=0.14\text{ m} \end{gathered}[/tex]Therefore the object is at 0.14 meters from the mirror.
