Question

State between two points of a concave mirror should an object be plaaced to get amagnification of -3

Answer 1

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An optical system with a magnification of -1 is said to be 4f. This means that the total track length from object to image is 4 times the focal length. For this mirror, the object and image are each 2f away from the mirror. For a concave mirror, the radius of curvature of the mirror, in the paraxial approximation if the mirror is not a sphere, is 2f, i.e., the focal length of a mirror is half the mirror radius. It's not a coincidence that the object location, image location and center of curvature are all equal. If you stand in front of a mirror at the center of that mirror, then light eminating from the center, radiating outwards hits the mirror at right angles, and from the law of reflection, retraces it's exact steps and comes back to focus where it started. Thus the object and image distances are the same, the system is 4f, and the object and image locations are each at the center of the mirror. Next time you look into a vanity mirror, place it next to a planar (the usual bathroom kind) and walk back until the two images are the same size. You will have then found the center of curvature of the vanity mirror.