Re: [Phys-l] index of refraction

[Hugh Haskell <hhaskell@mindspring.com>]

At 14:45 -0500 05/12/2009, Paul Lulai wrote:
> First, we do not do percent error calculations, but % difference 
> calculations.  I believe Hugh's comments are more directly 
> applicable to percent error calculations.  I might be wrong.

If the % difference is between your measured value and a "book" value 
(same as "accepted" value), the I see % difference and % error as the 
same thing, and the students will treat it as such.

> My students are to determine why the two values might be different. 
> I specifically state that we should not hold textbook values in too 
> high of a regard.

Never mind. They will hold the book value as "holy writ," and do 
whatever they can to get their results to agree with the book value.

> They must state what might cause these differences, how their 
> laboratory procedure might have caused these differences, and what 
> could be done to change the procedure to limit the error involved. 
> I do not give them the 'accepted' values of these substances.

OK. But if you give them a "book value" they will treat it as such. 
And if you give them something that has an "accepted value" to work 
with, they will, as you have clearly pointed out, find it on the 
internet or elsewhere, is that is what they will be looking for in 
the lab.

The solution to that is to not give them standard constants to 
evaluate in the lab.

> Kids today will google or Wikipedia the value.  If I don't ask them 
> to do a % diff, some (not all) will attempt to fudge data to match 
> the internet value.  I've done labs along these lines to determine 
> an unknown item in the past (maybe use n or C to determine what 
> solution or metal sample you have been handed).

If there is nothing for them to compare their result to, then they 
can't fudge their data to meet any predetermined answer.

> None of my labs are cookbook recipe labs.  I rarely conduct 
> verification labs.  However, students are becoming very adept at 
> finding some of the information that I ask them to determine.  Years 
> ago I would ask them to use a double slit to find the wavelength of 
> a laser.  Then kids could more easily find the wavelength.  I 
> switched to find the slit separation.  Now kids google the little 
> CAS image on the Cornell slides I've got and they know the openings 
> on the slides.  I now have to find a new version of Young's Double 
> slit.  Don't know what that will be, but it has never been a 
> verification lab.

CDs and DVDs make good slit sources, as do woven materials The 
diffraction patterns created by a nylon woven cloth (get one with as 
little stretch as possible, and the smooth fibers of nylon or other 
synthetics make much more uniform patterns) are very interesting and 
should pique the curiosity of at least a few of the students. Or use 
closely spaced razor blades to make a single slit with a different 
spacing for each group (stretching a nylon thread between the edges 
of the razor blade slit will turn it into  double slit) , or scratch 
slits on a painted microscope slide (the biologists might have some 
devices that will allow you to make well-defined scratches. All you 
have to be is a little cleverer than the students are and you should 
be able to provide them with material to measure that no one has 
knowledge of the results to be obtained.

One experiment that I like that connects macroscopic measurements 
with microscopic ones uses the nylon cloth as a starting point. They 
measure the thread spacing of the cloth by counting the threads in a 
distance large compared to the spot size of a laser beam. Then they 
use that spacing to measure the wavelength of the laser, and then use 
the wavelength thus measured to measure the groove spacing on a CD or 
DVD. It provides a direct connection between something that they can 
measure directly by eye and something that they cannot see at all.

One of the things I like to emphasize in introductory physics classes 
is the question "How do we know that?" So during the course of the 
year they see how we measure the scale of the solar system, using 
Kepler's laws and the parallax of asteroids to determine the distance 
to the sun (or the variation in the eclipse time of Saturn's 
moons--once we have a terrestrial measurement of the speed of light), 
then extending it to nearby stars using parallax, more distant stars 
using Cepheid variables and color-brightness scales, and finally to 
distant galaxies using red shift. We also discuss how to measure the 
size of atoms and other quantum particles so they get an idea of how 
we figure out what goes on in those areas where we cannot see or 
measure directly.

If there is one thing that I want my introductory students to take 
away from my class, it is the knowledge that the measuring of the 
very large and very small starts with very mundane measurements of 
ordinary things here on earth and uses those measurements as a 
jumping off point for all the rest. So they know that there is a 
connection between those things and our everyday reality, even if the 
connection is complex, it is a very human effort, and if they are 
interested, they can learn how to do it and make their own 
measurements, hopefully of things no one has measured before.

Too often students come away from science classes with the idea that 
this stuff is just magic, and no one really knows such things as the 
scale of the universe, or the size of atoms--it's all just made up 
stuff to confuse students. So it's important for them to see how we 
really can find some very interesting things out just using some 
everyday stuff and some careful thinking.

So they do need to measure some fundamental things, like g, and stuff 
like that, but I have them do it so early in the course that they 
don't really know what it is they are measuring until later when we 
put that information to good use. Meanwhile, they have had a 
smattering of experience with error analysis, and they understand 
that the values they got in the lab will need to be corrected later.

> I never spoke of using human error as a source of uncertainty.  I 
> wouldn't accept it any more than you would.

I didn't accuse you of that. I just tossed it out as a rule I enforce 
about error analysis. Too many of their prior teachers have used that 
to explain away crude results that don't agree very well with theory, 
so I do my best to squelch that tendency immediately.

> I am not sure what Hugh means by an accepted value of 0.
Any physical value that must be zero for certain situations or 
objects. For example, a collision in which the initial total momentum 
is zero. It must also be zero after the collision, but on an air 
track, it seldom is exactly zero due to factors that are very 
difficult to control. If you are asking them to calculate the % 
difference in before and after momentum, they will of necessity get 
an enormous value for that percentage. There are some physical 
properties of materials that have a theoretical value of exactly 
zero. Most of them are in advanced topics so first-year students are 
unlikely to encounter them but they exist. Measuring them involves a 
careful determination of the error bars of the experiment to 
determine if the theoretical value is included within the error bars. 
If so, there is no discrepancy with experiment and theory, so the 
experimenter will hope that they have narrowed the uncertainty in the 
experimental value. On the other hand, if the error bars do not 
include the theoretical value of zero, then it is important for the 
experimenter to be very sure that there is no remaining systematic 
error that can bring the value back to within the theoretical 
expectation, but if none is found, then something very important has 
been discovered--namely that there is something wrong with the 
theory. This is, of course, true for any theoretical value, not just 
ones that are presumed to be zero, but the zero values have a special 
nature in that one cannot identify the difference between experiment 
and theory with a percentage value.

A former student of mine, when she got to grad school, got into a 
project in which the goal was to measure the quadrupole moment of the 
electron, which is, I believe, supposed to be zero, indicating that 
the electron is a true point particle. Clearly, if the results came 
out to be unambiguously non-zero, no matter how small, it would 
change much of the current thinking about the nature of electrons. As 
to her results, alas, love intervened and she quit grad school to get 
married before the project got much off the ground. But I think that 
if anyone had found that the value is non-zero, we'd have all heard 
about it by now.

Of course, we can't expect students to discover everything. There 
isn't enough time in a one year course to cover the extent of 500 or 
so years of physics by doing everything in the lab. But they need to 
understand that everything they will have given to them over the 
course of the year, has its origin in exactly the sort of lab 
exercise that they have spend their lab periods doing over the course 
of the year. So we hope to give them at least a hint of what real 
science does, even if we can't take the time to recreate the entire 
process.

Hugh

--
Hugh Haskell
mailto:hugh@ieer.org
mailto:hhaskell@mindspring,.com

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