Light Waves and Colors Legacy Problem #2 Guided Solution
Problem*
The distance from the Earth to the sun is 1.496x1011 m. A solar flare occurs on the sun’s surface on Wednesday morning at 10:24 AM. At what time and on what day will electromagnetic radiation from the flare reach the Earth.
Audio Guided Solution
In this problem, an event takes place on the sun's surface at 1024 a.m. on Wednesday morning. The sun is 1.496 times 10 to the 11th meters from the earth. For an observer on earth to view this event, light from that event, the solar flare, must travel the 1.496 times 10 to the 11th meters distance to the earth in order for us to view it. If we wish to know the time of the day at which we will see that light, we need to find the time it takes, in minutes, for the light to travel that distance. So at the top of the page we observe that the speed of light is 2.998 times 10 to the 8th meters per second. We need to use that value in our calculation of time. The equation v equal d over t can be rearranged to the form t equal d over v, where t is the time and d is the distance and v is the speed of light. We can substitute 1.496 times 10 to the 11th meters, place it in the numerator, and we can put 2.998 times 10 to the 8th meters per second in the denominator. When we do, we'll calculate the time it takes for light to travel from the sun to the earth. It comes out to be 498.999 seconds, but we need to have it in minutes. So if we divide that value by 60, we'll get 8.317 minutes. We can take the 8 minutes and add it on to the 1024 AM. So this flare will be observed at 1032 AM on the same day.
Solution
10:32 AM on Wednesday (8 minutes later)
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.
Read About It!
Get more information on the topic of Light Waves and Colors at The Physics Classroom Tutorial.