[matmat]

gwnn, on Sep 21 2010, 09:05 AM, said:

it does seem harsh but why don't they say where they got the formula from?

There's always the possibility that they encountered this formula somewhere in their prior schooling; either in a chem class or an earlier physics class. They should still mention where it came from, but if it is something they saw not too long ago elsewhere, they might not feel the need to cite.

[kenberg]

I was a grad student in th sixties, a professor for quite a while. I have a couple points.

1. Ask the prof. what he would like. I think it is impossible for us to say because wwe did not read the problem. It souinds as if the point of the problem was to use data to get the result supported by the data. If that was the point and, important, it was clearly stated that this was what was wanted, then using any theoretical formula is not waht they were asked to do. There is theory, and there ar experimental results.

2. This concerns the working together versus cheating aspect, and I regard it as far more important than the problem. Some years back I was on a review panel for physics students accused of cheating on their lab report by working together. As you say, some working together was encouraged. The students' defense was that they had not at all disguised their common work and they were doing what they thought they were supposed to do. Some inquiry revealed that the professor, the graduate student, and the lab manual gave three substantially differing accounts of what proper practice was. The students' understanding seemed to be in reasonable conformance with one of these accounts. Of course they were judged to not be cheating. This led to some hard feelings about letting students get away with things. Lab reports are frequent sources of such problems. If there is any ambiguity at all in what is and is not allowed I hope it will be clarified immediately.

I will perhaps recite a couple of my favorite stories later, but dinner is on the table and my wife is not so patiently awaiting my presence.

[gwnn]

The formula appears to be correct after we have looked at it for about 15 minutes with my supervisor. The most likely explanation seems to be that someone found a similar problem online and just copied the final formula from it and plugged in our numbers. Then this formula spread around and two thirds used it finally. A problem like this has already been discussed and solved in a seminar before and nothing similar to the alien formula was ever written.

technical part: They used the idea that n-1 ~ p and did not use the refractive index given (n=1.0003 in 760mmHg).

[matmat]

gwnn, on Sep 21 2010, 06:52 PM, said:

technical part: They used the idea that n-1 ~ p and did not use the refractive index given (n=1.0003 in 760mmHg).

Lol... how did they get the prop. coefficient?

[Zelandakh]

Pick a random student at the start of the next class and ask them to solve a similar question on the blackboard alone. Chances are they will have simply copied the formula and will have absolutely no idea. Allowing this to continue is very bad practise as it encourages the students not to actually learn which tends to be bad come the final exam. If there is no final exam (coursework assessment) then it is even worse since you are not giving a fair mark to all students.

[Ant590]

Zelandakh, on Sep 22 2010, 06:34 AM, said:

Pick a random student at the start of the next class and ask them to solve a similar question on the blackboard alone.

Isn't this the kind of thing that will ensure you have a class of 0 to teach in the future?

[Ant590]

gwnn, on Sep 20 2010, 11:02 PM, said:

Students are allowed to cooperate but it's not really encouraged. In practice it helps my grading since these study groups usually hand in their assignments next to each other in the pile and they're almost always identical and I just need to skim through them.

There should be a plagiarism policy at the institution. To my gut, the system you have is unworkable; you might as well have students handing in one assignment per group.

[gwnn]

matmat, on Sep 22 2010, 01:23 AM, said:

gwnn, on Sep 21 2010, 06:52 PM, said:

technical part: They used the idea that n-1 ~ p and did not use the refractive index given (n=1.0003 in 760mmHg).

Lol... how did they get the prop. coefficient?

The experiment involved a Michelson-Morley interferometer with a small reservoir of air in front of one of the mirrors.

Point a) gave them how many orders the interference pattern move if you moved one of the mirrors by a certain small length. This gave them the wavelength of the laser they were working with.

In point b) some air was removed from the reservoir and again it was given to them how many orders the patterns were moved.

The data given to them by the professor was:
-refractive index at normal pressure
-the number of orders the interference pattern was moved
-the air pressure initially and finally
-not given but everyone correctly calculated it) the wavelength of the laser

Now you can use only 1, 2 and 4 (you just calculate the phase shift that was caused by a lower n)

Or, using Helene's formula, use only 1 and 3, ignoring Michelson and Morley altogether and solving it with good accuracy.

However they used 1, 3 and 4!! The formula is

n=1+m*lambda*p/(2*L*dp)

Where
lambda is the wavelength
p and dp is the pressure and change in pressure
L is the length of the reservoir (multiplied by 2 because the laser passes twice)
m is the number of orders difference between the two patterns

But this is really not a "general knowledge formula" not like using a slightly unknown trigonometric identity that you found in a strange Russian book, this is a formula that is applicable only to this specific problem and which definitely needs some justification.

[P_Marlowe]

gwnn, on Sep 22 2010, 03:20 AM, said:

<snip>
But this is really not a "general knowledge formula" not like using a slightly unknown trigonometric identity that you found in a strange Russian book, this is a formula that is applicable only to this specific problem and which definitely needs some justification.

This answers your question.

The usage of this formula needs to be justified, i.e. ommiting the justifications
is an error, i.e. the works is not complete.
The correct answer is just guess work, it is like picking a random number and
it turned out to be the right one.

In Mathematics, guessing a solution is a valid technique, but you still need to
verify, that the solution is correct.

Getting a solution and verifying a solution are two parts, and they are quite often
independ.

With kind regards
Marlowe

[phil_20686]

gwnn, on Sep 22 2010, 03:20 AM, said:

 
But this is really not a "general knowledge formula" not like using a slightly unknown trigonometric identity that you found in a strange Russian book, this is a formula that is applicable only to this specific problem and which definitely needs some justification.

i used to get into trouble for this kind of thing:

The formula n-1 prop p is completely obvious to anyone with some schooling. After all, the way light travels in a low density is that it travels from a-b getting absorbed and re-emitted by light along the way. Thus provided the density of atoms is low enough that there is no significant intermolecular forces, the time it takes from a to b is time in a vacuum plus time delay per atom*individual atom. Thus provided that you keep the frequency of light and the composition of the gas the same, clearly n-1 = p. I would have simply prefaced my answer with "Trivially" and expected this to convey that I knew what I am talking about - that seems to be accepted practice among academics .

Also, i did you the experiment in the most efficient way possible, since the measurement of the refractive index will be far more accurate the the measurement of how far the pattern moved, generally.

[gwnn]

But the formula they gave is only based on (n-1)~p, it is refined and modified to fit the data they had in the experiment that was described. If anyone had included the justification (with the starting point of n-1~p) or had just given n=1+0.0003*544/760, I would have been extremely happy to give them maximum points.

For your convenience, here is the formula they used again:
n=1+m*lambda*p/(2*L*dp)

do you think this is a general knowledge and trivial formula? Would you give it like this, with no justification?

[kenberg]

Many of the responses you are receiving are from people who are far more on top of the details than I am. It's been a while for me. But...

Here is from your initial post:

"There is a problem that is worth 4 points. Almost everyone got point a) right using exactly the technique the professor had in mind.

It's the "had in mind" part that can cause trouble.

In a much more elementary course we were given the usual instruction about conversion of units. There were weekly quizzes and one question told us to compute the angular velocity of the Earth about its axis. Knowing what was wanted I worked it out in radians per second. My friend Greg noted that the units were not specified and wrote down 1 revolution per day and went on to the next problem. He received full credit.

The point here is that either the prof has made some stipulations about what was wanted or he hasn't. It matters.

This matter of bringing in formulas from the net, or from space, or whatever, also has to be addressed. Since retiring I have taught this and that here and there, and a couple of years ago I was teaching a course where one of the students regarded all homework assignments as invitations to spend far too much time on the web and far too little time thinking. I didn't want to forbid the use of the internet but I didn't think of the course as "How to find answers on the net" either. With a little thought I mostly was able to handle this. Partly some straight talk is useful: The purpose of homework is not to get the answers for the prof, he already knows the answers. The purpose of homework is to learn the correct way to think about the material. There will always be a few who have enormous capacity to be oblivious to this obvious remark, but most, after they think about it, get the point.

[helene_t]

kenberg, on Sep 22 2010, 01:45 PM, said:

My friend Greg noted that the units were not specified and wrote down 1 revolution per day and went on to the next problem. He received full credit.

He shouldn't. Assuming the angular velocity asked for is relative to an initial system, it is roughly 365.24/364.24 revolutions per day.

[kenberg]

helene_t, on Sep 22 2010, 07:59 AM, said:

kenberg, on Sep 22 2010, 01:45 PM, said:

My friend Greg noted that the units were not specified and wrote down 1 revolution per day and went on to the next problem. He received full credit.

He shouldn't. Assuming the angular velocity asked for is relative to an initial system, it is roughly 365.24/364.24 revolutions per day.

Yes, I understand. But he should get as much credit (maybe more) than those of us who started from 1 revolution per day and converted it to radians per second!

This sort of gimmicky situation is at least slightly relevant to the OP. Almost every problem posed on an exam has some sort of context. I think profs and textbook writers regularly abuse this and end up asking questions that have far too much of a "You know what I mean" flavor. Sometimes (in the ang vel problem) it's just amusing, sometimes I really didn't know what they mean. A complex variables problem was stated as "Find the values of z for which the following power series converges". I spent 30 seconds finding the radius of convergence and a great deal of time trying to determine which values of z on the boundary gave convergence. The intended question was to determine the radius!

Oh for the fun days of grad school. One of my favorite memories is my assignment to grade a graduate course in PDEs, a course I had never had. I took it as a point of pride to not complain. This was probably not a good thing for the students in the course.

[Winstonm]

jdonn, on Sep 20 2010, 04:21 PM, said:

Call me cynical but it sounds like the students are cheating, or are they allowed to copy off each other's assignments? It's unthinkable that 5/9 students would by coincidence use a formula you hadn't been taught in class and gotten identical answers with it, whether the answer they got is right or wrong.

There's always ONE conspiracy nut in the crowd.

[phil_20686]

So this morning, over breakfast, I have produced a derivation and a theory. I know. I'm a geek. But I'm a theoretical physicist so what can I do

if n-1 prop p then
dn prop dp with the same proportionality, so

n = 1 + p*dn/dp

for a cavity of length 2L the difference in the number of wavelengths (caveat - I only really remember stuff about fabry-pelon inferometers so assume that it is true for others) will be:

m/2L = 1/lambda - 1/lambda'

using lambda vacuum = n*lambda, we trivially obtain:

dn = m*lambda vaccum/2L

and hence:

n = 1+m*lambda vacuum/(2L) * p/dp

Now lambda vacuum = lambda original*n original, so for small changes in pressure this will be right to order n but pick up an error of order n^2-1

This is interesting as I'm sure that had it come from a text book on theory it would have contained this small correction, thus, I suspect that it comes from a lab book. Is it possible that they have done a related experiment? I seem to remember that some fabry pelon interferometer have an evacuated cavity, and that you have to calibrate for the wavelength because you laser changes or some such. In that case, and if you have experiment by recipe which we had, you might well hav a formula that drops the small correction, and students might well think they could quote a formula that appears in a lab book.

[gwnn]

nice proof

My supervisor asked the kids where they got the formula from; one girl answered that she found it on the internet, and the others didn't say anything.

It was weird because generally they like to write in their homework where they found one information or another (a girl solved an optics problem correctly using a real plane mirror and her Dad experimentally (what is the minimum distance from you to a person so you can see his whole body in your plane mirror) - she didn't quite get the right answer but she got maximum credits anyway).

[matmat]

gwnn, on Sep 23 2010, 05:10 AM, said:

It was weird because generally they like to write in their homework where they found one information or another

I think there is somewhat of a stigma associated with using the internet as a reference.