TABLE II – Diffraction Angle Uncertainties, Wavelengths, and Relative Errors
SPECTRAL LINES
Atom
Type
Line
Color
DIFFRACTION
ANGLE
UNCERTAINTY
||
(minutes) (rad)
For Instructions see page 2.
Measured

Handbook

(nm)
(nm)
Observed
Relative
Error
Predicted
Relative
Error
  '
'
(see part d)
a) To obtain the “Diffraction Angle Uncertainty”, do the following. For each
Hydrogen line, write down the magnitude of the DIFFERENCE between
(left) and (ave). This gives you a measure of the amount by which the
angular readings for Hydrogen are uncertain. Pick the LARGEST of these
differences and use it as the uncertainty for ALL the Hydrogen lines. (If all
differences are zero, use 1 minute of arc as a default value for the smallest
difference.) Report this both in units of minutes and of radians. Similarly,
obtain a value of  appropriate for the Mercury and Mystery measurements
of the second lab period (one value of  for the full set of measurements for
Part II).
b) “Measured ” values are calculated from the grating equation using (ave) as
the diffraction angle. “Handbook ” values are obtained from page 4 (last
week’s instructions). Because the mystery lamp wavelengths are not given,
you will have to leave that entry for “Handbook ” blank.
c) “Observed relative error” is defined as:
  '
'
d) “Predicted Relative Error” is determined from uncertainties present in this
experiment. The calculated wavelength depends only on the diffraction angle
and the grating spacing. By differentiating the grating equation, we find that
the relative uncertainty in wavelength depends on the uncertainties in angle
and grating spacing as follows:



s
s

cos 

sin 
“s” is the grating constant given on your grating, “s” for these gratings is 0.3
lines/mm. “” is (ave) reported in Table I, and “” is the diffraction angle
uncertainty – MEASURED IN RADIANS – reported in another column to the
left. Make certain that you can see how this calculation works. When
involved in measurements in other labs or eventually in your life’s work, you
will be asked to specify uncertainties in measurements and related
calculations. This is how it’s done.