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The floor of the room is linoleum, which certainly reflected some of the light, as well as metal tables and chairs around the room. However, there was certainly potential for reflected light to find its way into the light sensor. For the most part, barring the occasional printer light or computer power button, there were no external light sources present. I used the large, darkened physics classroom at my school to gather data.
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All of my measured values were slightly higher than those calculated through the equation, and I think reflected light is to blame for this. My data affirmed my hypothesis in that the intensity of light did decrease at the projected rate, very close to an exact trend.Īlthough my data was decently accurate, there were a few key sources of error. The linearized graph helped to strengthen my data and my procedure, and provides an easy way to assess the accuracy of my data. The data I collected was decently accurate, ~3.9% error, and reflected a hyperbolic trend proportional to 1/r2. I was successful in testing and affirming the Inverse Square Law with reference to Light. I calculated error for all my data points and averaged them to get ~3.9% error. Was used to give a mathematical approximation for the target value of my experiment.Įrror I took the difference between my calculated and measured data, and divided that by the calculated data to get a value for the percent error. It can be simplified by removing the distance squared and leaving the 4πin the numerator.Īs an example, for the 1.5 meter reading,įor the Expected Values shown above, the equation Where the Intensity, in Watts / m², is equal to the Illuminance, in Lux, times the surface area, in m², divided by the luminous efficacy, in Lumens / Watt, times the squared distance, in m². The best way to represent this data is in watts per meter squared The sensor measured the luminous flux per square meter in Lux, which equals one lumen per square meter. I had to use multiple conversions and calculations to reconcile my data. I am measuring the intensity of light using a fixed light sensor.Ĭontrols: ambient light in the room, wattage of bulb, increment of measurement, reflective surfaces in the room, reflective potential of my body, angle of lightbulb, height of lightbulb. I am going to be incrementally increasing the distance between the light source and the fixed light sensor to get a smooth graph showing the 1/r2 relationship. If I measure the intensity of light at a given distance of r, it will decrease proportionally to the inverse of the distance squared. The aim in this investigation is to determine whether the intensity of light decreases as a proportion of the inverse of the distance squared, and I hypothesise that the real-world results will reconcile with the math. This makes the intensity of light proportional, the proportion is 1/(4π), to the inverse of the distance squared. If the intensity was measured one meter away from the light source, the intensity would be the power (S) divided by 4π times 1 squared. This works because the Power output of the light source has to be divided by the surface area it has to cover. Simple geometry can tell us the proportion to be divided by, within the inverse square, is the surface area of a sphere at a given distance (4πr²) This did not only explain that light decreases over a distance, common knowledge at the time, but that it decreases at a specific proportion to the inverse of the distance squared. He did this by showing that the intensity of light (I) at a given distance from the origin of the light was the power output of the light source (S) was proportional to inverse of the squared distance. Although the inverse square law applies to sound, gravity, and electric fields, Bullialdus focused on light to test this theory. He found that the forces on Jupiter and Saturn, exerted by the sun, were proportional to the inverse of the distance squared. Newton also dabbled with the Inverse Square Law in his study of gravity, where he measured the periods and diameters of the orbits of Jupiter and Saturn.
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The prediction holds with other massless particles, and explains the inverse square law of gravitational force.