# Using a Spectroscope

In our spectroscope labs we will be using a manual spectroscope will a
resolution allowing wavelength determination to better than 1nm. Although
this unit is somewhat more difficult to use than direct-reading spectroscopes
it is far more precise.

# Theory

This spectroscope uses a diffraction grating to split incoming light into
it's component colours. By determining the angle at which these components
exit the grating, the exact wavelength may be determined.

For a diffraction grating the angle at which a component wavelength diffracts
is determined by the formula:

We may rearrange this formula to solve for wavelength. The distance between ruled lines in the grating, d, is easily computed since we know that the grating in our spectroscope is 7500 lines/inch. Converting to meters, d=3.387*10^{-6}m. All we need do is measure the angle at which the component is observed to diffract and solve for wavelength. Usually first order (m=1) is used but other orders may be observed for better dispersion (and hence more accurate observations).

The Diffraction Grating from the HyperPhysics site. An
excellent explanation.

# Spectroscope Components

Light from the source is directed towards the entrance slit. It is then
focussed by a lens onto the diffraction grating. Components are split and
exit the grating at an angle as shown. Individual components may be identified by aligning a crosshair inside the eyepiece with the line and reading the angle
from the vernier scale. Before a line is observed the telescopes (both
entrance and observation) should be focussed to provide a sharp image. Simply
turn the lens on each to adjust. As well, the slit is adjustable.

# Calibration

NEW
Before using the unit it must be calibrated as follows:
- Install the grating with the wording facing the eyepiece telescope
- Align the eyepiece telescope so that it is directly in-line with the entrance telescope (i.e. zero degrees offset) by rotating it until the image of the source slit is seen. If a white light source is used, the line will appear white.
- Lock the eyepiece telescope using LOCK A in the figure
- The grating plate (and lock B in the diagram) are already set. DO NOT
TAMPER WITH LOCK B
- Accurately read the offset from the vernier. This represents ZERO DEGREES and must be added or subtracted from the angular reading of each unknown line
- Unlock the eyepiece telescope (LOCK A) allowing it to rotate freely

Readings obtained are now referenced against the value read at the "zero" degree mark. If, for example, the "zero" reading was actually 60.0 degrees an unknown line at 70.1 degrees is hence actually 10.1 degrees grating angle.

# Operation

To begin, orient the source so that light falls on the entrance slit. Open the
slit to allow a good deal of light through. Now rotate the eyepiece telescope
so that the entrance slit is visible and focus both lenses to provide a sharp
image of the source. Rotate the eyepiece until the line of interest is in
sight. Using the fine adjustment screws under the baseplate (on the eyepiece
side ... do not loosen the grating plate lock), carefully center
the line of interest on the crosshairs. It may be necessary to reduce the size
of the slit to get a precise image here as well. An example of what you'll see
through the eyepiece appears to the left. The angle of the telescope
relative to the incoming light may now be read.

The vernier scale allows the angle to be read to an accuracy of about 0.05
degrees. Begin by reading the integer of the angle directly - in the above
example this is 19 degrees. Use the next smallest number below the line
pointed-to by the arrow ("1" in the figure shown). Next, the fractional
angle can be read using the vernier. Simply floow the lines across on the
vernier scale (the outside) until you locate the ONE which best lines-up
with a line (any line) on the circular inner scale. In our example above,
the eigth line (corresponding to 0.8 degrees) is best aligned with a line
on the inner ring. To either side of this line (e.g. 0.7 or 0.9) you'll see
that the lines do not match. Finally we add our integer angle of 19 to our
vernier angle of 0.8 to get an angle of 19.8 degrees. It is possible that
two lines will be 'best aligned' in which case read between them for an
accuracy of 0.05 degrees. We may now substitute into the formula above
to yield an answer of 566 nm (See __Csele, Fundamentals of Light Sources and Lasers__ page 24).
Note that this is second order - if first order was assumed you'd get an answer in the infrared which is highly unlikely unless
you are not human :).