An object is placed in front of a circular mirror with a radius of curvature of 6 cm. A virtual image is formed 8 cm from the mirror. If the object and mirror are kept at the same location, but the radius of curvature is changed such that after is it is changed, the image formed is the opposite orientation as the image of the first radius and the magnification is 3.1 times smaller (the second image is 3.1 times smaller than the first image), what does the radius of curvature need to be in cm?
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