LAB: Bragg Diffraction Grazing Angle Error

[Gemini_Cricket]

Homework Statement

I wasn't sure where to post this question. I hope I picked the right section of the forums. This is from intermediate lab. The lab is for Bragg diffraction using microwaves. The grazing angle is a measured quantity along with the voltage (which was measured using an oscilloscope). The uncertainty on the voltage is estimated. The grazing angle that is recorded is from the angle indicated on the turntable disk that the reflection cube (crystal) sits on.

Homework Equations

Not sure if the Bragg equation is needed but here it is:
n*(wavelength) = 2*(plane spacing)*sin(grazing angle)

The Attempt at a Solution

Okay, so I assumed that the uncertainty in the grazing angle would be the uncertainty in the measurement, however my professor told me to measure the error in the angle by the error in the voltage. I have no idea what he means by this. I know about error propagation and the different equations, but have no clue how to use the error in the voltage and translate that to error in the angle.

One data set is 3 degrees at a voltage of 290 +/- 1. Any ideas?

 

[mfb]

Please describe the whole setup.
Which voltage? What does that voltage mean?

 

[Gemini_Cricket]

Okay I'll try to make it short. There's a microwave transmitter, it transmits microwave radiation onto a foam cube of steel chrome balls that act as scattering centers. There is a receiver on the other side that picks up the radiation after it is reflected. The turntable that the cube sits on can be rotated at specific angle intervals. Data is recorded for a number of angles. The voltage is as measured by the oscilloscope. The peaks in the voltage correspond to the maximum reflection angles. Since the grazing angles are measured directly I would think that the uncertainty would just be human measurement error, but apparently that is not the case.

 

[mfb]

Ah, so voltage is a measurement of the reflected intensity for a given angle. Well, then you have two sources of uncertainty, the angle and the voltages. If there is a reasonable peak visible in the data, I think I would fit a function to that peak, otherwise I would estimate the peak position in some other way (depends on the setup then). This will include both the statistic uncertainty for the angle and the uncertainty for the voltage, and then the systematic uncertainty for the angle can be added afterwards.

 

[Nickie]

Hello,

Thank you for reaching out for assistance with your lab. It is great that you are taking the time to think about the uncertainties in your measurements and how they may affect your results.

Firstly, it is important to understand that the uncertainty in the grazing angle is not solely dependent on the measurement error, but also on the accuracy of the turntable disk and the reflection cube. Therefore, it is important to consider all sources of error when determining the uncertainty in the grazing angle.

In terms of your professor's suggestion to use the error in the voltage to estimate the error in the angle, this could be due to the fact that the voltage measurement is likely more precise than the angle measurement. In other words, the voltage measurement may have a smaller uncertainty compared to the angle measurement. Therefore, by using the error in the voltage, you can potentially get a more accurate estimate of the uncertainty in the angle.

To do this, you can use the Bragg equation and the error propagation formula to calculate the uncertainty in the grazing angle. You can use the measured voltage value and its uncertainty to calculate the uncertainty in the wavelength, and then use that to calculate the uncertainty in the grazing angle.

It is also important to consider the significance of the uncertainty in your results. If the uncertainty is relatively small compared to the measured value, then it may not significantly affect your results. However, if the uncertainty is large, it is important to acknowledge this in your analysis and discuss how it may affect your conclusions.

I hope this helps guide you in your analysis. Good luck with your lab!