Reflection and Mirrors Legacy Problem #11 Guided Solution
Problem*
Every morning Bob Gillette uses a shaving mirror with a focal length of 72 cm to view the image of his face. Supposing his face is 18 cm from the mirror, determine the image distance and the magnification of his face.
Audio Guided Solution
This question demands that we use the mirror equation and the magnification equation in order to determine the image distance and the magnification value. We are given that there is a mirror with a focal length of 72 cm, and we are given that an object is placed 18 cm from the mirror. To solve for the image distance, we use the mirror equation, rearranging it to the form 1 over di, or image distance, is equal to 1 over f, for focal length, minus 1 over do, for object distance. We substitute in values of 72 and 18 into the equation and it turns into 1 over di equals 1 over 72 minus 1 over 18. Evaluating the right side of the equation on my calculator gives me point, or negative point, 0, 4, 1, 6, 6, 6, continuing. And so that's the image, the reciprocal of the image distance, and if I wish to find the image distance, I simply take the reciprocal of the right side of the equation. It becomes negative 24 exactly. So the answer to what is the image distance is negative 24 cm. To find the magnification, I need to understand that the magnification is defined as the negative of the di value divided by the do value. And if I take the di value, negative 24, and I divide it by the do value of 18, and then take the negative of it, I get 1.3 repeating, which I can round to 1.3, and that's the magnification. It tells me how many times bigger that the image is than the object.
Solution
di = -24 cm
Magnification = 1.33
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(\descriptive{d_o}{d_o,distance object} = 24.2\unit{cm}\); \(\descriptive{d_i}{d_i,distance image} = 16.8\unit{cm}\); \(\descriptive{f}{f,focal length} = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use. Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
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