Reflection and Mirrors Legacy Problem #7 Guided Solution
Problem*
A spherical concave mirror has a radius of curvature of +62 cm. What is the focal length of the mirror?
Audio Guided Solution
We can think of a spherical concave mirror as being a section of a sphere, and being a sphere, it has a radius, or a radius of curvature. That is, that's the radius of the sphere from which we can imagine the mirror has been sectioned off. And the inside of the sphere has been coated, making it a concave mirror. And here in this question, the radius of curvature is 62 centimeters. And when they ask what is the focal length, what we have to remember is that the focal length is simply the midpoint between the center of that sphere and the surface of the mirror. And so it happens to be one-half the radius, or 31 centimeters.
Solution
+31 cm
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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