Light Waves and Colors Legacy Problem #4 Guided Solution
Problem*
The German-born, American physicist Albert Michelson devoted much of his life to the accurate measurement of the speed of light. In 1923, he positioned mirrors and detectors on two different California mountains positioned nearly 35 km (nearly 22 miles) apart. Using a sophisticated timing method of involving the rotating of octagonal mirrors, Michelson determined the speed of light to be 299,774 km/sec. At this speed, estimate the time it takes light to travel 35 km between mountains.
Audio Guided Solution
In the early 1920s, Albert Michelson determined the speed of light. He used a method in which he positioned two mirrors on mountains approximately 35 kilometers apart. Light traveled from one mountain to the other, bounced off a mirror, and came back. By rotating one of the mirrors at just the right speed, he was able to get the mirror to rotate one-eighth of a rotation in such a manner that the face, the next face of the mirror, was pointing straight back at his mountain from which he shined the light from. The result of his method was that he determined the speed of light to be 299,774 kilometers per second. The mountains are 35 kilometers apart. Determine the time it takes to travel from one mountain to the other mountain. We need to use the equation speed equals distance over time. We can rearrange the equation to solve for t. It becomes t equals distance divided by speed. Dividing the distance of 35 kilometers by the 299,774 kilometers per second gives us the time in seconds. It comes out to be 1.1675 times 10 to the negative 4 seconds. We can round that to two significant digits such that it becomes 1.2 times 10 to the negative 4 seconds.
Solution
1.2 x 10-4 s or 120 µs
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 and record in an organized manner, often times they can be recorded on the diagram itself. Equate given values to the symbols used to represent the corresponding quantity (e.g., \(\descriptive{v}{v,velocity} = \num{3e8}\unit{\meter\per\second}\), \(\descriptive{λ}{λ,wavelength} = 554 \unit{\nano\meter}\), \(\descriptive{f}{f,frequency} = \colorbox{gray}{Unknown}\)).
- 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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