PASCO OS-8539 Educational Spectrophotometer - Manual (Page 17)

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M o d e l N o . O S - 8 5 3 7 a n d O S - 8 5 3 9 P r o c e d u r e s
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If a dim spectral line only appears on one side of the central ray (“zeroth order”), calculate where the central ray
is using a brighter spectral line that is visible on both sides of the central ray. Then determine the angle from the
central ray to the dim line to find the angle,
, for that spectral line (Fig. 24).
Calibrating the Grating
The number of grating lines on the Grating is approximately 600 lines per millimeter. This translates to a Grating
line spacing of d = 1666 nm (1.666…x10
-6 m).
To find the exact Grating line spacing, use a sodium lamp to calibrate the Grating. The average wavelength, , of
the yellow sodium doublet is 589.3 nm. Solving m  = d sin  for the line spacing, d, assuming m = 1 (for the first
order) gives
d = /sin 
where  is the known wavelength of the sodium doublet. To determine the angle, , find the difference in angle
between the two first order yellow lines and divide by two.
Using the calibrated Grating line spacing, d, the wavelength of any spectral line in any other spectrum can be
more accurately determined using m
 = d sin where the order, m, is 0,1,2,…
Angular Resolution
When the Rotary Motion Sensor is fastened to the lower set of holes on the hinge on the Spectrophotometer Base
(as described earlier), the small diameter post of the Pinion will make contact with the edge of the Degree Plate.
The shaft of the Rotary Motion Sensor will rotate approximately 60 times for every rotation of the Degree Plate
(or 360½). One rotation of the Rotary Motion Sensor shaft represents approximately 6½ of angular displacement
of the Degree Plate. The maximum resolution of the Rotary Motion Sensor is 1440 divisions per rotation. Since
one rotation is 6½, the angular resolution is 6½ divided by 1440, or one quarter of a minute (0.25’) or fifteen sec-
onds of arc. This translates to a wavelength resolution of 2 nm, given a grating line spacing of approximately
1666 nm for the Diffraction Grating included with the Spectrophotometer.
If the Rotary Motion Sensor is fastened to the upper set of holes on the hinge, the larger diameter part of the Pin-
ion will make contact with the edge of the Degree Plate. The shaft of the sensor will rotate 15 times for every
rotation of the Degree Plate. The maximum angular resolution is one minute or sixty seconds of arc. This trans-
lates to a wavelength resolution of 8 nm, given a grating line spacing of approximately 1666 nm.
Central ray
(“zeroth order”)
For example, measure
the difference in angle
between these two
lines. One half of the
difference is the angle
to use for calculating
the wavelength.
Figure 24: Measure the Angles for both First Order Spectral Patterns