Reflection and Mirrors Legacy Problem #8 Guided Solution
Problem*
A decorative garden sphere has a diameter of 44 cm. The reflecting surface of the shiny sphere makes a great convex mirror. What is the focal point of the convex surface?
Audio Guided Solution
In this question we have a garden sphere which has a diameter of 44 centimeters, and if you have ever seen one of these garden spheres you know that they make great reflectors. They act as convex spherical mirrors, and if the diameter of the sphere is 44 centimeters then what we know is that the radius is 22 centimeters, and 22 centimeters radius for that convex mirror would mean that the focal point is simply one half the radius value, which would make it 11 centimeters. Only in the case of convex surfaces we imagine that that focal point is located behind the surface, so we insert a little negative sign in front of the 11 to indicate that the focal length is negative 11 centimeters.
Solution
-11 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.
Read About It!
Get more information on the topic of Reflection and Mirrors at The Physics Classroom Tutorial.