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# Lab 1: Light and Distance

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### Abstract

In this lab a sensor was used to determine the relationship between light intensity and the distance between the light source and the sensor to determine that as distance increases, illumination decreases as a polynomial function. The reason for the diminishing in brightness is due to the dispersion of light rays that decreases the number of rays that eventually end up being perceived by the sensor.

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### Terms and Definitions

Lux: A unit of illumination

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### Overview of Lab

The lab uses a light source of invariable intensity and a light sensor on a track. The light sensor is moved away from the light source by 10 cm increments and records the intensity of light in lux. Any data taken either by hand or on the computer

The purpose was to determine a mathematical relationship between intensity of light and the distance between the sensor and light source.

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### Data

#### Observations, Notes

In general, as the distance between the light source and the detector increases, the illumination decreases. Light from outisde of the system likely interferred, contributing to the break in this trend at long distances.

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### Equations and Calculations

The illumination decreases until the ambient light makes the light variance, due to distance, negligible.

[(7.097 * 10^4)/(D^2)] + 64.54
Where D is the distance between the light and the sensor

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### Analysis and Conclusion

We learned that as a sensor is moved farther away from the light source, the perception of illumination is lowered. The light disperses from the light source, decreasing the number of light rays that are percepted, be it by a digital sensor or biological one (i.e. your eye). However, the at some distance, the light perceived by the source is negligible compared to the ambient light of, for example, the sun. The relationship between distance and illumination perceived is a polynomial function.

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### Lab Extension

1. Do some research into the unit "Lux". How does it compare to lumens or watts? How does the sensitivity of the human eye come into play? A good starting point might be the hyperphysics website.

Lux is the unit used to measure luminous flux/unit area and is the same as lumen/m^2. Lux is used in to determine if a surface is luminous enough for human activities such as reading which require visual interpretation. This is measure through finding the power/ unit area of a surface with respect to how it is perceived by the human eye. Lumens is total radiant power in watts divided by the sensitivity of the human eye. The formal equation is: Luminous flux in lumens = Radiant power (watts) x 683 lumens/watt x luminous efficacy. Luminous flux is a part of the power perceived as light by the human eye whereas lux is the power/ unit area of an illuminated surface.

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### Pictures and Diagrams

The light source is on the left and the light sensor is the clear tube protruding from the disc on the right.
Overview of the lab setup.