Measuring Quantities

This is a very rushed outline.

Young modulus	Y = s/s, where s(stress)=F/A, s(strain)=dL/L_o. It's best to draw a graph of s against s and find the gradient of the straight line section before you reach the yield point (where it goes plastic). The difficult thing to measure is dL. This is given by dL=FL/AY. Y is huge (»100 GPa), so to make dL measurable you need to design the experiment with a big L and small A (i.e. a long thin wire). Even then you'll need a calibrated eyepiece (at the very least) to measure the extension. This was one of the first experiments we did this year. L, being large, is easy to measure, but the small A needs a delicate instrument : a screw gauge or an electronic vernier will measure the diameter to the nearest 0.01 mm, but you'd better take measurements at several places and calculate an average. Of course, you will need to use halving and pr² to convert the diameter to an area, and you need to take care with units.
Conductivity	G=I/V (NB letter 'eye' not figure 'one') and G=sA/L, so s(conductivity this time)=IL/VA. The determination is probably best done by plotting a current-voltage graph and then multiplying the gradient by the appropriate geometrical factor. If you are dealing with a good conductor, you are going to be plagued with high currents and low voltages, so you really want to get the conductance down as low as possible by increasing L and reducing A. The same considerations apply to the measurements as in the Young modulus case discussed above. You'll need a standard electrical circuit with a variable power source (cell in parallel with a potentiometer) connected to an ammeter and the wire under test, with a high-impedance voltmeter across the wire. You want the resistance of the specimen to be sufficiently high for the contact resistances between the ends of the specimen and the circuit not to be significant.
Resistivity	Exactly the same considerations apply as for Conductivity, but you need to adapt the details to cope with everything being the other way up.
Refractive index	n = sinq_air/sinq_medium= 1/sinq_critical. The best thing is to measure some angles and plot a graph, the gradient of which will give n. A ray of light can be traced on paper before it enters a glass block and after it emerges. You have to join the two lines thus drawn after removing the block in order to find where the ray inside the block went. Remember that all angles have to be measured relative to the normal. Make sure you've read the refraction page.