Spectrometer vernier scale. Quick answer

[teleport]

Spectrometer vernier scale. Quick answer please!

This is a quick question. I am measuring the emission spectra for hydrogen, but now I'm finding myself wondering about measurements in the vernier scale. I have the right and left angle measurements; however they differ by more than 180 degrees. The ones on the left side are cloe to 360, while the ones on the right side are from 20 to 60 degrees. To make the angle correction what would I need to substract to what? Thanks

 

[ZapperZ]

In the diffraction formula, where are these angles measured from? There is a position that is the reference "0 degree" position.

Hint: you will need to know the angular position of the zero'th order.

Zz.

 

[teleport]

I get it, but I don't have the scale in front of me right now. Is the zero'th order just 360 degrees (is this regular?)?

 

[teleport]

Now I vaguely remember the TA said something about 180 degrees. Could it be this is the position of the zero'th order? i.e. is that regular?

 

[cesiumfrog]

Despite the title of your question, it doesn't sound like you're asking about the vernier scale specifically.

In the past I've demonstrated a diffraction spectrometer lab in which the apparatus happened to have *two* (vernier, incidentally) scales, one on each side. Frequently students made the mistake of inconsistently recording some data from one scale, and some data from the *other* scale. This sounds like your problem.

I told those students that they should redo the experiment for accuracy, but it did turn out that the scales happened to be calibrated "almost exactly" 180 degrees apart. If something like that is the case, anybody can figure out how to roughly correct their original data simply by drawing a diagram of the experiment from above (a circle with the 360 degrees of markings, the grating in the middle, coloured lines for each ray..), but to do so without checking the calibration yourself is effectively falsifying data. (I just hope you learn the lesson, which is to keep a much better log book, and think before you do the experiment. Then ask the necessary questions when the assistant/demonstrator arrives.)

 

[teleport]

Hmm, I remeber this very well. It was mentioned in the lab, but I'm almost 100% sure I used only one of the two scales. I don't think that is my problem. This is because the TA mentioned we would have to make the correction for the angle, assuming we had not made the error you mention. It is probably just what ZZ mentioned, but I do not recall the zeroth. This is my problem.

 

[ZapperZ]

I do not know what kind of a spectrometer you are given, so I have no idea how the scales are oriented.

In experiments like this, there is a good reason why you are asked to measure on both sides. Just think, you actually need just the position on ONE side, in principle to get the value of the frequency or wavelength. So why are they making you measure both sides? This is because there could have been some error in the positioning of the instrument, in the positioning of the diffraction grating, etc... that many not properly align the interference lines with the scale on the instrument. What I mean here is that if the dead center of the instrument is, let's say, 0 degrees, a slight misalignment could cause the 0th order to be at, say, 3 degrees to the left.

So we tend to ask the students to measure both sides, take the difference, and divide by two. Hopefully, if there's any misalignment, the error for this can be minimized. Alternatively, one can also figure out where the zeroth order is, and subtract (or add) the off-zero value to all the values being measured. That would produce more or less the same result.

Zz.

 

[teleport]

Yes, however, I have degrees like 356 on the left side, and 25 on the other side, both for the same line on order 1. When I subtract them and divide by 2 it gives me the angle 165 which is huge for order 1. So I probably need to make some adjustment to the angle. What correction is that?

 

[teleport]

Is it just (25 + 360 - 356)/2 ? Makes sense to me. Confirmation?

 

[jtbell]

In the past I've demonstrated a diffraction spectrometer lab in which the apparatus happened to have *two* (vernier, incidentally) scales, one on each side.

If this is like the Pasco spectrometers that we use, those two scales are for reducing or eliminating error due to eccentricity in the bearings that the scales rotate on. You're supposed to read both scales, reduce one reading by 180 degrees to make them consistent, then find the average of the two readings. Usually they differ by at most a few minutes of arc after reducing one of them.

Then, if you're using a diffraction grating rather than a prism, you're supposed to repeat this procedure for the same line as it appears on both sides of the central axis, and find the average of the (absolute value of) the two diffraction angles, measured from the central axis.