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The distance between the image and the mirror is -8.6 cm
A concave mirror has a reflective surface that is curved inward and away from the light source. Concave mirrors reflect light inward to one focal point.
Unlike convex mirrors, the image formed by a concave mirror shows different image types depending on the distance between the object and the mirror.
Let's use the mirror equation to solve the problem:
[tex]\dfrac{1}{f}=\dfrac{1}{d_o}+\dfrac{1}{d_i}[/tex]
where f is the focal length of the mirror, the distance of the object from the mirror, and the distance of the image from the mirror.
For a concave mirror, for the sign convention f is considered to be positive. So we can solve the equation for by using the numbers given in the text of the problem:
[tex]\dfrac{1}{12}=\dfrac{1}{5}+\dfrac{1}{d_i}[/tex]
[tex]\dfrac{1}{d_i}=-\dfrac{7}{60}[/tex]
[tex]d_i=-8.6\ cm[/tex]
Where the negative sign means that the image is virtual, so it is located behind the mirror, at 8.6 cm from the center of the mirror.
Hence the distance between the image and the mirror is -8.6 cm
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