Lab Exercise - Crossed Polarizers
![[url=https://commons.wikimedia.org/w/index.php?search=photoresistor&title=Special%3ASearch&go=Go#/media/File:Photoresistors_-_three_sizes_-_mm_scale.jpg]"Photoresistors"[/url] by Junkyardsparkle is in the [url=http://creativecommons.org/publicdomain/zero/1.0/]Public Domain, CC0[/url]
Three photoresistors shown with a millimeter scale below. We will use such a component to measure light intensity today.](https://www.geogebra.org/resource/U2tnnjjT/wfLFlbcNfGVUPMcE/material-U2tnnjjT.png)
Background
Here are a few facts I hope you recall from our discussions of polarizers:
* Unpolarized light will be attenuated by 50% after passing through a single polarizer. This reduction will not depend on the orientation of the polarizer.
* Putting a second polarizer in line with the first one and rotating the second polarizer such that there is an angle between their transmission axes results in a further attenuation by a factor of
* Light that is already polarized either by natural means or by a polarizing filter will change intensity according to the aforementioned equation when viewed through a polarizing filter as you rotate the filter.
LDR (Links are underlined below)
We will be using a light-dependent resistor (LDR), which is also called a photoresistor, to measure light intensity today. The LDR is made of a semiconductor, which implies the material is an electrical insulator under normal conditions, and yet with a little energy input, electrons get promoted from being stuck in atomic orbitals into what's called the conduction band where they are free to conduct electricity. The little energy to do this is the laser light we are shining on the LDR. The more laser light, the more free electrons, the better a conductor it becomes. The multi-meter's whole job is to measure how much the LDR resists the conduction of electricity. That resistance is inversely proportional to the light intensity incident on the LDR, allowing us to use it as a light intensity meter. To know the value of the light intensity in Lumens (the usual unit), we'd have to carefully calibrate the LDRs. As a decent rule, the relationship between light intensity in lux to resistance is:
Procedure
- Set up a laser, two in-line polarizing filters and the LDR on a stand.
- If possible, adjust the beam so that the whole surface of the LDR is covered by laser light.
- Remove the polarizer closer to the LDR and slowly rotate the other filter while observing the laser dot on the LDR. Q1: What do you observe, and what does it indicate to you about the laser light?
- Hook up your LDR to a multi-meter in resistance mode, and observe the effect of rotating the polarizer on the values of resistance measured. Q2: Does the resistance value rise or fall when the light gets brighter?
- If it seems like beyond a certain brightness there is no measurable or obvious change in the resistance, make the laser just a bit dimmer than that level by rotating the polarizer and then leave it there.
- Replace the second polarizer on the bench and rotate it until the spot on the LDR is as bright as possible. (Note: You will NOT be moving the filter closer to the laser again during the experiment.) Q3: In this orientation, how are the two polarizer's transmission axes related?
- Starting from the brightest spot, start entering values into the GeoGebra spreadsheet (not Excel, since custom curve fitting is much harder in Excel). Make the first column degrees of rotation and the second column the value of resistance.
- Rotate the filter 10 degrees at a time while carefully measuring the resistance. Do this for one full rotation of the filter.
- Create a third column in the spreadsheet and set it equal to This column contains values proportional to the intensity of the light.
- Create a list of data points made of the first and third columns of data (angle and intensity).
- Create a function in GeoGebra that according to our physics discusson should match the intensity vs angle data. Make the slider ranges precise enough and with appropriate ranges to be able to fit the data. Q4: What is the function that you are entering?
- Take a shot at fitting the curve by hand by adjusting the sliders. If it won't work at all, recheck your equation and slider values/ranges.
- Use the fit function in GeoGebra to fit the data automatically. You will choose the list of points and specify a function for which you'll enter your custom function. Q5: According to your eyeball, does it fit the data pretty well? If not, raise your hand so I can check your work.
- To quantify the goodness of fit, one often uses the coefficient of determination, or R2 for short. It is a value between zero and one. Zero implies no relation between the function and the data and one implies a perfect fit. The function to get this value in GeoGebra is called
RSquare. Q5: What is your R2 value?
Additional Questions
Refer to the Wikipedia site linked above to answer the following questions:
Q6: What is the ratio of light intensity on a sunny day to a dark overcast day?
Q7: What is the ratio for a sunny day to a moonless night? Isn't it crazy that your eyes deal with such variation!
Q8: According to your data, what was the brightest and dimmest values for the laser light falling on the LDR?
Please submit all your data, curve fits with displayed regression lines and answers to these questions in digital format (either .docx or .pdf) on Edmodo before next week's lab.