**Introduction:**

Experiment to mathematically model the relationship between a flashlight’s distance and the size of its projection.

Hypothesis: As the flashlight moves further away from the wall, the diameter of the light projected onto the wall will grow exponentially.

**The Data:**

Linear relationship visualized:

Measurements:

#1 | 2 | 5/8 |

#2 | 12 | 3+3/8 |

#3 | 24 | 7 |

#4 | 36 | 10+1/4 |

#5 | 48 | 13 |

#6 | 60 | 16+1/2 |

#7 | 72 | 19+1/2 |

#8 | 84 | 23 |

#9 | 96 | 26+1/2 |

#10 | 108 | 29 |

#11 | 120 | 33 |

**The Data Format**

The first number is the measurement identifier. The second number is the distance of the tip of the flashlight from the base of the wall in inches. The third number is the diameter of the circle of light projected onto the wall by the flashlight in inches.

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**Methodology**

I placed a flashlight on the floor pointed toward that wall. I used a tape measure to place the flashlight away from the wall in increments of one foot (except for the first measurement in which I placed the flashlight two inches away from the wall so that I had room to measure the light projection). The distance measurements were from the tip (the point closest to the wall) of the flashlight to the base of the wall. After the flashlight was situated, I recorded how far away it was from the wall, then I would leave the flashlight in its place and only move the tape measure. I would then measure the diameter, horizontally, of the light projected onto the wall. This number was then recorded as the dependent variable next to the measurement of the flashlight’s distance from the wall.

**Conclusion**

The relationship between the dependent and independent variable appears to be linear, and thus my hypothesis was incorrect. Averaging both data sets yields a ratio of 11/3, which is approximately 3.5:1. This means that for every 3.5 inches the flashlight moves away from the wall, the diameter of its projection grows by one inch.

**Advice for Creating Your Own Experiment**

- Consider what you are trying to measure.
- Evaluate the set of tools at your disposal.
- Select the unit(s) of measure.
- Devise a data format/container.

In order to see how one might accomplish some goal, simply slow down and observe what is around. This experiment taught me how much one can learn from simple tools applied in simple ways.

**References**

Contact Daniel Rode for references: drode@student.cccs.edu

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