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I am a retired science teacher and a grandfather. I am trying to help my grandson complete this project.
The experiment is not difficult but there is no clear explanation of the equation. E = 375.81/R1.034
What do the numbers represent and specifically how is it completed once the resistance is determined?
Thanks for any help. DGTeacher
How Does the Intensity of Light Change with Distance?
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Re: How Does the Intensity of Light Change with Distance?
Hi BlueHawk44,
We sent the following message as a reply to your email - please let us know if that email didn't go through (if so, we apologize). Pasting the full reply here so others can see it as well. In case you didn't see it yet, there is a very brief explanation of this equation on the "Make it Your Own" tab of the project:
https://www.sciencebuddies.org/science- ... eityourown
Here's the more detailed explanation from our email:
The equation is derived from the graph labeled "Typical Resistance vs Variable Illumination" on the photoresistor's datasheet:
https://www.sciencebuddies.org/science- ... asheet.pdf
Depending on what grade your grandson is in, he is probably familiar with the equation for a line (usually expressed as y = m*x + b) on a graph with linear axes. However, if you look at the graph on the datasheet you will see that it has a logarithmic scale on both axes (e.g. they go 1, 10, 100 instead of 10, 20, 30...). A plot with logarithmic scales for both axes is called a log-log plot for short. Again, depending on what grade your grandson is in, he might not have encountered logarithms in math class yet. The equation for a straight line on a log-log plot is
y = a*x^k
where a is the y-intercept of the line and k is the slope of the line (for more information and some examples, see this page https://en.wikipedia.org/wiki/Log%E2%80%93log_plot). So in the case of the equation
E = 375.81 / R^1.084
the y-intercept of the line is 375.81, and the slope of the line is -1.084.
The last part is also a bit of algebra your grandson may or may not have seen yet:
x ^ (-k) = 1/(x^k)
trying to put that in words: x to a negative number is equal to one over x to that number. So the slope of the line is negative 1.084, we can write that as 1/R^1.084 instead of R^(-1.084). But it would also be valid to write the equation as
E = 375.81 * R^(-1.084)
To be clear, the numbers 375.81 and 1.084 are specific to this photoresistor. If you bought a different photoresistor, you would need to look at its datasheet to get the slope and intercept of the line. The purpose of this equation is to convert resistance (what you are actually measuring) to lux (the unit of light measurement). It's important not to get this equation mixed up with the inverse square law, which describes how light intensity changes with distance from the source.
Hope that helps,
Ben
We sent the following message as a reply to your email - please let us know if that email didn't go through (if so, we apologize). Pasting the full reply here so others can see it as well. In case you didn't see it yet, there is a very brief explanation of this equation on the "Make it Your Own" tab of the project:
https://www.sciencebuddies.org/science- ... eityourown
Here's the more detailed explanation from our email:
The equation is derived from the graph labeled "Typical Resistance vs Variable Illumination" on the photoresistor's datasheet:
https://www.sciencebuddies.org/science- ... asheet.pdf
Depending on what grade your grandson is in, he is probably familiar with the equation for a line (usually expressed as y = m*x + b) on a graph with linear axes. However, if you look at the graph on the datasheet you will see that it has a logarithmic scale on both axes (e.g. they go 1, 10, 100 instead of 10, 20, 30...). A plot with logarithmic scales for both axes is called a log-log plot for short. Again, depending on what grade your grandson is in, he might not have encountered logarithms in math class yet. The equation for a straight line on a log-log plot is
y = a*x^k
where a is the y-intercept of the line and k is the slope of the line (for more information and some examples, see this page https://en.wikipedia.org/wiki/Log%E2%80%93log_plot). So in the case of the equation
E = 375.81 / R^1.084
the y-intercept of the line is 375.81, and the slope of the line is -1.084.
The last part is also a bit of algebra your grandson may or may not have seen yet:
x ^ (-k) = 1/(x^k)
trying to put that in words: x to a negative number is equal to one over x to that number. So the slope of the line is negative 1.084, we can write that as 1/R^1.084 instead of R^(-1.084). But it would also be valid to write the equation as
E = 375.81 * R^(-1.084)
To be clear, the numbers 375.81 and 1.084 are specific to this photoresistor. If you bought a different photoresistor, you would need to look at its datasheet to get the slope and intercept of the line. The purpose of this equation is to convert resistance (what you are actually measuring) to lux (the unit of light measurement). It's important not to get this equation mixed up with the inverse square law, which describes how light intensity changes with distance from the source.
Hope that helps,
Ben