Physics 132 Lab Lab #4 Thickness of Hair Experimental Design 1. What is the null hypothesis for this lab? What is your alternative hypothesis? A null hypothesis would be there is no significant difference between measuring with a caliper or using diffraction. An alternative hypothesis is there is a significant difference in measuring with a caliper rather than measuring using diffraction. 2. Which set of measurements do you think will be ‘better’? How will you define a set of measurement being ‘better’ than the other? A set of measurements is ‘better’ than another set, when it is both more accurate (referring to the closeness of a measured value to a standard or known value) and more precise (referring to the closeness of two or more measurements to each other). I think the ‘better’ measurement will be diffraction because it’s more technical and should render more precise measurements. Measuring with the Caliper 3. Measure the thickness of the hair using the calipers, measuring to the nearest 0.01 mm. Get a measurement from everyone at your table, for a total of four measurements. Don’t share your measurements until after everyone has done one; it’s important that your measurements don’t influence one another. Name Measurement (mm) John 0.09 Mateo 0.05 Vikki 0.03 Darren 0.06 4. Calculate the mean and standard deviation of these measurements; this will be one of your sets of data for this lab. 0.025 is the standard deviation. 0.0575 mm is the mean. Measuring with Diffraction With this experiment, we will be using a strand of hair to create a double slit to generate interference of light. Let’s take a closer look at what’s going on. The difference between the physical path lengths for a double slit is:There is a slight difference for our situation. With the hair, what we have is a double slit with the slits being really (infinitely) wide. When this fact is taken into account using calculus, we get a factor of two popping up underneath the d, so we have: 5. Create an equation for in terms of the distance between the center to the first dark spot, , and the distance from the hair to the screen, . d = 650nmsin(⌒tan( ))yh 6. After mounting the hair to the platform, look at the position of the hair on the track. What factors might contribute to the uncertainty in the hair’s position? Think about how the hair is placed onto the track, and the method in which you are measuring it’s position. Hair is 71 cm from the screen. Because the hair is so small and we had to tape it in place, and it is not rigid, the actual location of the hair on the track could be greater or less than 71 cm by 1-2 millimeters. 7. Consider how much uncertainty each factor contributes to your measurement. For example, consider the position of the base of the stand with the hair. How accurate do you think the placement is? By about how much do you think you might be off by? Do this for each factor contributing to the uncertainty. There could be uncertainty in the position of the base of the stand because it may not be exactly vertical so depending on whether or not it is tilted on the track can change the position of the hair by about 1 mm due to the hair being higher that the base of the stand. 8. Estimate your total uncertainty for this position. It is generally better to make your estimate error on the higher side, although it is also important to keep your uncertainty within a reasonable amount as well. Thetotal uncertainty could be about roughly 1-2 mm. 9. Use the interference pattern to measure the thickness of the hair by looking at the distance between the first two dark spots to either side of the central bright spot. Have each team member at your table measure the distance independently; make sure to only share your measurements after everyone has made their measurement. Since you’re measuring the distance between the dark spots, divide by two to get the distance from the dark spot to the center. Name Measurement (mm) Thickness of hair (mm) John 4 0.115 Mateo 8 0.058 Vikki 3.5 0.132 Darren 4.5 0.103 10. Why do you think we asked you to measure dark-to-dark instead of from the center line to the first dark spot? Measuring from dark spot to dark spot would be more accurate because the distance is so small. It is also difficult to tell where the edge of the center bright spot is because it is so bright. 11. Calculate the mean and standard deviation for this set of measurements. The mean is 5 mm and the standard deviation is 2.04. We can now proceed to measure the thickness of the hair using interference. However, our measurement has two sources of uncertainty: the distance from the hair to the screen and the distance from the central max to the first dark spot. We need to propagate these uncertainties into our final measurement on the width of the hair. From question X you can see that the equation to get from and to the thickness is complex (sines and tangents!). In this case, the simplest thing to do is to use the Monte Carlo method from the library lab to find the uncertainty. This time, you will be creating your own simulations using a spreadsheet. 12. Create a Monte Carlo simulation for the thickness of the hair using Google sheets, and attach it to this lab. Feel free to reference the previous simulation used in the library lab. a. The monte carlo simulation portion is attached in the moodle submissions of this lab report 13. From the spreadsheet, calculate the mean and standard deviation of the thickness of the hair from diffraction. The mean is 0.111 mm and the standard deviation is 0.137. Comparing the Measurements Now that we have both sets of data, let’s determine if these two methods produce statistically different measurements. For this, we’ll turn to the t-test. 14. Before we perform the t-test, do you think your measurements will be statistically different or statistically equivalent? Justify your reasoning. We think that our measurements will be statistically different becausethe Monte Carlo method provides a wider range of data. To do the t-test, we need to calculate a t-value for or sets of data, and then compare it to a t-value corresponding to the p-value that we are looking for, in our case 0.05, and the number of degrees of freedom. For this lab, you can use the table here. This table refers to the p-value adraws an alpha level, but
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