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# A production-line inspector wants a mirror that produces an image that is upright with a magnification of 7.5 when it is located 14.0 mm from a machine part. a. What kind of mirror would do this job? b. What is its radius of curvature?

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In this problem, we need to find the type of mirror (concave $f>0$ or convex $f<0$) (part $a$), and its radius (part $b$). We know that the image is upright ($h_{i}>0$). Also, we know the magnification and the position of the object. To solve the problem, we are going to use several equations, the mirror equation $\frac{1}{f}= \frac{1}{d_{o}}+ \frac{1}{d_{i}}$, the magnification equation $M= -\frac{d_{i}}{d_{o}}= \frac{h_{i}}{h_{o}}$ and the relation between the focal length and the radius $r=2f$

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