## Mechanical Resolution Of The Phasmatron Spectroscope

### Version 1.0 of 6/3/2004-8:10 a.m.

The mechanical resolution is determined by the minimum angle ÄN by which the viewing telescope can turn. For PHASMATRON's angle measuring devices, this is 10-3 degrees (a millionth of a degree). Converting to radians, ÄN=1.74532*10-5 rad. Next we need dE/dë so we can approximate Äë.

We know that dE/dn=2/cos{sin-1(nD/2)}. This for nD=1.72803 gives:
dE/dn=3.9724624 rad. (In the area of sodium D), and
dn/dë=1.2702*10-5/A. (again in the area of sodium D)
=> dE/dë=(dE/dn)(dn/dë)=5.04582*10-5 rad/A. Therefore we can approximate and use ÄE/Äë=5.04582*10-5 rad/A, and since ÄE almost eqs ÄN, Äë=ÄN/5.04582*10-5 rad/A. For ÄN=1.74532*10-5 rad, this gives:

Äëmechanical=0.3458942A. (In the area of the D lines)
Compare this with Äëoptical=0.3866148A. (In the area of the sodium D lines).
(The TRUE mechanical resolution can be calculated using the program in section Measuring Wavelengths. If you input N=60°, M=59.097° and on another run input N=60° and M=59.098°, you can subtract the two wavelength values found and get thus the Äë. This way you will get that the true mechanical resolution in the area of sodium lines is 0.3564453A, which is very close to the value of Äëmechanical found above.)

Suppose you wanted to calculate instead the mechanical resolution in the area of the blue mercury line. (4358.35A) Then:

dn/dë=(1.76197-1.74805)/|4358.35-4799.9107|=3.1524545*10-5/A.