Reflection and Mirrors Legacy Problem #14 Guided Solution

An effective problem solver reads the problem carefully and identifies the known information, equating it with variables in known physics equations, then identifies unknown information and plots out a strategy as to get from the known quantities to the unknown quantities. Applying this strategy to this problem, we recognize that the eyelashes are an object that is placed in front of a concave mirror. The length or dimension of the eyelashes are 1.2 centimeters, and that's what we would call HO, or height of object. They are magnified to 1.6 centimeters when looked at in the mirror, and that's what we would call the image height, or image dimension. We'll say HI equals 1.6 centimeters. This occurs when the eyelashes are placed 5.8 centimeters from the mirror, the eyelashes are the object, and this is the object distance, so we would say DO, or DO, equals 5.8 centimeters. We're looking for the image distance, DI, and the focal length, F. In order to solve for the image distance, I need to use the equation that goes HI divided by HO equals the negative of DI divided by DO. Substituting values into this equation yields 1.6 centimeters divided by 1.2 centimeters equals the negative of DI divided by 5.8 centimeters. Multiplying each side of the equation by 5.8 yields an answer for DI of negative 7.7383 centimeters. The negative simply means, on the opposite side of the mirror, a virtual image. So the image distance is negative 7.7 centimeters when rounded. In order to find the focal length, I need to use the mirror equation, which states 1 over F equals 1 over DO plus 1 over DI. DO is 5.8 centimeters, and DI is negative 7.7333 centimeters. So substituting into the equation, I get 1 over F equals 1 over 5.8 plus 1 divided by negative 7.7333. That gives me a value of 0.0431033 repeating, and if I take the reciprocal of that number, I end up getting a focal length of 23.2 centimeters.