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Home Spectra, Refractive Indices, and WaveLengths The Spectrometer Measurements with the Spectrometer Measurement of the WaveLength of Light  
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Measurement of the WaveLength of Light
A diffraction grating consists of a number of fine lines ruled at equal distances apart on a plate of glass  a transmission grating; or of speculum metal  a reflexion grating. We will consider the former. If a parallel pencil of homogeneous light fall normally on such a grating, the origin of light being a slit parallel to the lines of the grating, a series of diffracted images of the slit will be seen, and if θ_{n} be the deviation of the light which forms the n^{th} image, reckoning from the direction of the incident light, d the distance between the centres of two consecutive lines of the grating, and λ the wavelength, we have
The quantity d is generally taken as known, being determined at the time of ruling the grating. The spectrometer is used to determine θ_{n}.
Turn the table carrying the grating so as to allow the direct light to pass it; adjust the telescope so that the vertical crosswire bisects the image of the slit seen directly, and read the vernier. This gives us the direct reading. Place the grating with its plane accurately perpendicular to the incident rays, as described above, and turn the telescope to view the diffracted images in turn, taking the corresponding readings of the vernier. The difference between these and the direct reading gives us the deviations θ_{1}, θ_{2}, &c. A series of diffracted images will be formed on each side of the direct rays. Turn the telescope to view the second series, and we get another set of values of the deviation θ_{1}', θ_{2}', &c. If we had made all our adjustments and observations with absolute accuracy, the corresponding values θ_{1}, θ_{1}', &c., would have been the same; as it is their mean will be more accurate than either. Take the mean and substitute in the formula
We thus obtain a set of values of λ. If the light be not homogeneous, we get, instead of the separate images of the slit, more or less continuous spectra, crossed it may be, as in the case of the solar spectrum, by dark lines, or consisting, if the incandescent body be gas at a low pressure, of a series of bright lines. In some cases it is most convenient to place the grating so that the light falls on it at a known angle, φ say. Let ψ be the angle which the diffracted beam makes with the normal to the grating, and θ the deviation for the n^{th} image, φ and ψ being measured on the same side of the normal, then it may be shown that
and
The case of greatest practical importance is when the deviation is a minimum, and then φ = ψ = θ/2, so that if θ_{n} denote the minimum deviation for the n^{th} diffracted image, we have
In the case of a reflexion grating, if φ and ψ denote the angles between the normal and the incident and reflected rays respectively, φ and ψ now being measured on opposite sides of the normal, the formula becomes
and if θ be the deviation
If the value of d be unknown, it may be possible to find it with a microscope of high power and a micrometer eyepiece. A better method is to use the grating to measure θ_{n} for light of a known wavelength. Then in the formula, nλ = dsinθ_{n} we know λ, n, and θ_{n}, and can therefore determine d. Experiment.  Determine by means of the given grating the wavelength of the given homogeneous light.
Values of deviations, each the mean of three observations:


Home Spectra, Refractive Indices, and WaveLengths The Spectrometer Measurements with the Spectrometer Measurement of the WaveLength of Light 