Why Is Alaska So Cool? Activity 7 Answer Key

Activity 7: Angle Intensity Investigator

Answer Key

1.  What is your sinusoidal regression equation and correlation coefficient? Record these values in your daily log as well. Use labels or descriptions appropriately. Include the equation generated by the TI-83 as well as that generated by Excel.
Your log should show values, such as:
Y = .5054142072186 * sin(.03704524640497X + 1.9725789649705) + .47130785853923
Your model equation will be different (unless you use the default values in the calculator's ANGLE program).

2.  Did you accurately predict the type of equation and graph that would best represent the intensity of light as the distance from the light source increases? If not, what type of equation did you predict?
Ideally, you predicted a sinusoidal regression.

3.  Using any of the analytical methods discussed elsewhere (evaluating for function, creating a table of values, tracing the graph), determine the intensity at 35°. Which method did you use?
Using the data from our investigation, the intensity at 35o would be approximately 0.407 mW/cm2. Your answer will surely be different, but should be reasonably within the limits of your investigation. If you used the ANGLE program's default "Use Sample" data, then your answer should be the same as indicated here.

4.  Consider carefully: We stated earlier that in the real world, it is unreasonable to associate increases of angle of incidence beyond 90° with further changes of intensity. Why is this unreasonable? (Hint: If you put the light sensor at 100°, what would be the angle of incidence?)
At the exact moment of sunrise and of sunset the angle of incidence for each of these is 90o. It is unreasonable to think direct sunlight intensity values would vary for angles of incidence greater than 90o or less than -90o, because those are angles beyond which the sun is below the horizon. It is either morning before sunrise, or evening after sunset.
But wait! If you continue to take light intensity measurements into the evening after sunset, you would note that intensity continues to diminish through dusk until complete nighttime darkness. There would be a corresponding increase of light intensity in early dawn before sunrise. (At any rate, south of the arctic circle in summertime we would find this phenomenon, right?) Now, doesn't this show that intensity continues to change with changing angles of incidence?
No. These intensity readings clearly are not due to angle of incidence changes because there is no sun in the sky now. Remember, the angle of incidence is relative to the normal, and concerns light coming directly to a surface from some source. Dusk and early dawn twilights, however, are not due to direct sunlight, and therefore there is no associated normal by which to measure the angle of incidence. The intensity change must be due to some other cause.
For your further consideration: (a) What is the cause that produces the phenomena of dusk, twilight, or the dawn's early light? (b) Related to the same cause, how long does it take the moon's sky to become completely dark after sunset? How long before sunrise on the moon does the moon's sky start becoming light.

5.  What does your investigation of light intensity relative to angle of incidence suggest to you about temperatures in Alaska relative to temperatures in Mexico in the summertime?
(a) If we may assume that (1) temperature is directly related to sunlight intensity, and if we may assume that (2) intensity is related to the angle of incidence, then it would be a reasonable hypothesis that noon temperatures at higher latitudes are lower on average than noon temperatures at lower latitudes. So, we may conjecture that since Alaska is at higher latitude than is Mexico, Alaska is cooler than Mexico at a lower latitude where the sun is directly overhead at noon.
Why does it suggest this to you?
(b) The rationale for this hypothesis is that the solar noon angle of incidence increases at higher latitudes relative to the solar noon angle of incidence at lower latitudes.

Print a copy of the Excel graph to include in your project report.
Your Excel plot should be similar to the plot on your graphing calculator.

See the sample data spreadsheet.

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