In our spectroscopy labs we will be using a manual spectroscope will a resolution allowing wavelength determination to within a few nanometers. Although this unit is somewhat more difficult to use than direct-reading spectroscopes it is far more precise.
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*10-6m. 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.
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.
Before using the unit it must be calibrated as follows:
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.
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 seventh line (corresponding to 0.7 degrees) is best aligned with a line on the inner ring. To either side of this line (e.g. 0.5 or 0.9) you'll see that the lines do not match. Finally we add our integer angle of 19 to our verneir angle of 0.7 to get an angle of 19.7 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 571 nm. 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 :).