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What is the radius of curvature of a concave mirror that magnifies an object by a factor of -3.2 when the object is placed 20 cm from the mirror?

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In this problem, we have a concave mirror, and we need to find the radius of the mirror. We are going to use three equations, the mirror equation 1f=1do+1di\frac{1}{f} = \frac{1}{d_{o}}+ \frac{1}{d_{i}} where ff is the focal length of mirror, dod_{o} is the position of our object, and did_{i} is the position of image. Also, we are going to use the magnification equation to find the image height M=dido=hihoM= -\frac{d_{i}}{d_{o}}= \frac{h_{i}}{h_{o}} Furthermore, we are going to find the radius from the equation r=2fr=2f

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