Answer:
0.29
Explanation:
We can find the position of the image by using the mirror equation:
[tex]\frac{1}{f}=\frac{1}{p}+\frac{1}{q}[/tex]
where:
f is the focal length of the mirror
p is the distance of the object from the mirror
q is the distance of the image from the mirror
For the mirror in this problem:
f = -12.7 cm (the focal length of a convex mirror is negative)
p = 31.3 cm (distance of the object)
Solving for q, we find the position of the image:
[tex]\frac{1}{q}=\frac{1}{f}-\frac{1}{p}=\frac{1}{-12.7}-\frac{1}{31.3}=-0.111 cm^{-1}\\q=\frac{1}{-0.111}=-9.1 cm[/tex]
And so, the magnification of the image is:
[tex]M=-\frac{q}{p}[/tex]
And substituting,
[tex]M=-\frac{-9.1}{31.3}=0.29[/tex]
Which means that the image is upright (positive sign) and diminished (M is smaller than 1).
