Reflection and Mirrors Legacy Problem #21 Guided Solution

It is the habit of an effective problem solver to read a problem very carefully, identifying known information in terms of the variables in common physics equations, identifying the unknown information, then planning a strategy as to how to get from the known to the unknown. Here in this problem I read about an image distance from a mirror by 26.9 centimeters. It's described as a virtual image, and that's not a trivial description. It's telling me that this image is behind the mirror, and as such, has an image distance which is negative. So from reading the first clause of this sentence, I'm left with the understanding that dI equal negative 26.9 centimeters. The mirror itself has a radius of curvature of 48.1 centimeters, and that radius is related to the focal length. The focal length is always one-half the radius of curvature, and as such, while R equal 48.1 centimeters, the F equal 24.05 centimeters. What I wish to calculate is the object distance. So this becomes a mirror equation problem, which I rearrange it in order to solve for object distance. I say 1 over del for object distance equal 1 over F for focal length minus 1 over image distance, or dI for image distance. I substitute in values of 24.05 centimeters for F and negative 26.9 centimeters for dI, and then I go about evaluating the right side of the equation, which comes to 0.078755. That's not the object distance, that's the reciprocal of the object distance. If I take the reciprocal of this number, I'll get the object distance, and it comes out to be 12.6976, and I can round that to three significant digits.