Introduction To Spectrometer: Glass Prism And Diffraction Grating

Theory

Introduction

A spectrometer is an instrument used in the analyses of the spectra of radiations. The glass-prism spectrometer is ideal in taking measurements of ray deviations as well as refractive indices. At times, diffraction grating may be used instead of the prims in the study of optical spectra. A prism is capable of refracting light into one spectrum while diffraction grating spreads the available light in numerous spectra (Duarte 2015). Due to this, slit images that are formed using a prism are mostly brighter as compared to the ones formed through grating. The only challenge in this is that the enhanced brightness of the spectral lines is often offset through a decreased resolution as the prism cannot effectively separate the various lines as the case of grating. However, these brighter lines permit a slit width that is narrow in shape to be used which is partially able to compensate for the lowered resolution (Guanter et al., 2015).

Theory

There is no direct proportionality between the angle of refraction and the wavelength of light in a prism. For this reason, the measurement of the wavelengths using a prism is achieved through the construction a calibration graph of the deviation angle against the wavelength and using the source of light with a known spectrum. The wavelength of the unknown spectral lines can thus be interpolated from the obtained graph (Hadni 2016). Future determinations of wavelengths is validated upon the creation of  a calibration graph for th prism and this is only possible if they are made from prism that is aligned precisely just the same it was at the time of production of the graph. To achieve the reproduction of such an alignment, all the measurements must be made when the prism is aligned to enable refracting the light at the angle of the lowest possible deviation.

The light that is studied is rendered parallel using a collimator that is composed of a tube that has a slit of adjustable width at an end and a convex lens at the other end. The collimator must be maintained in a highly focused through the adjustment of the position of the slit to the point at which it is at the focal point of the lens (Hartmann et al., 2014). The parallel beams that originate from the collimator are made to pass through a glass prism that is on a prism table which is rotatable, levelized, lowered or even raised. The prism then deviates the components colours of the released light through various amounts and spectrum so generated is examined through the use of a telescope that is mounted on a rotating arm and oscillates over the divided angular scale.

The theory of the prism spectrometer illustrates that a spectrum that has maximum definition is achieved when the light ray angular deviation of the light ray that goes through the prism is least. Under such conditions it can be demonstrated that they ray goes through the prism is a symmetrical manner. For a specific wavelength of light that is traversing a certain prism, that exists a characteristic incidence angle for which the deviation angle is least. This angle is dependent in the refractive index of the prism and the angle that is formed between the two sides of the prism that have been traversed by light (Hossain et al., 2015). The equation below is used in illustrating the relationship between the two variables

Methods

in which n is the refractive index of the prism,  the angle formed between the two sides of the prism that has been traversed by light and A the angle of minimum deviation.

Methods

1. The sodium lamp was turned on and allowed to warm up for more than 10 minutes
2. The prism was positioned on the prism table having the unpolished side flush with the holder of the prism and then locked into place (Leedle et al., 2015)
3. The telescopes was rotated to the straight through position
4. The slit adjust was open to provide a wide yellow line through the telescope
5. The slit adjust was then closed to provide a sharp narrow yellow line
6. The prism table lock was ascertained to be released in an anticlockwise manner and then the prism table rotated until it was in the position as illustrated in the diagram.
7. The telescope lock was ascertained to be released in an anticlockwise directed and then the telescope rotated until the spectral lines were noticed.
8. The position of the minimum deviation was obtainable through the rotation of the prism table in one direction only where the spectral lines would seem to move across the field of view, stop and the move in a reverse direction (Mouroulis et al., 2014)
9. The cross hairs of the telescope were lined up on the red spectral line and the prism table lock released and the prism table rotated until there was a change in position of the spectral line. The prism table was then locked when it occurred
10. The telescope was position close to the spectral line and the telescope fine adjust was then used in lining up the cross hairs on the line
11. The reading on the scale was noted which was the angle A of the spectral line
12. The parts 10-11 of the procedure were repeated for the other five string lines
13. The wavelength and the colour were noted for each of the lines measured
14. Steps 9-13 were repeated to estimate the average value

Note: The prism has to be moved to position B and the telescope moved to the B angle position as illustrated in figure 2 in order to perform the next section

1. Parts 3-14 of the method were repeated
2. The results were tabulated
3. The minimum angle of deviation, D, was then determined for every line through subtracting the mean of the smaller angle from the mean of the greater angle and then halving the result
4. A calibration curve was constructed of the minimum deviation angle against the wavelength (Piascik et al., 2014)
5. The prism spectrometer was used in the examination of the spectra of the other sources of light that were available in the laboratory. Comparison was made with the tabulated values

Diffraction Grating Procedure

1. The prims were substituted with the transmission diffraction grating that was supplied in which the grating was fixed to the prism table surface with the clamp given.
2. The sodium spectra generated on either side of the straight-through position was determined using the eye while the grating was aligned about perpendicular to the collimator
3. The telescope was rotated to the position of the first order spectrum on one of the side and then the cross hairs aligned with the spectral line. The angular setting of the telescope was taken care of.
4. The procedure was repeated for as numerous lines as possible for the first order spectra
5. Another set of spectral lines known as second order would be observed upon an increase in the angle beyond the first order spectra lines

Note: Performing the next section of this experiment required moving the telescope to B angle position

1. The Parts 3-5 of the method were repeated
2. A table illustrating the angular setting for every line on the right as well as left of the straight line through position was then drawn. The ? was determined for both the first order and second order lines through  finding the difference between the smaller angle and the larger angle and the final answer divided by two (Squires, Constable & Lewis (2015)
3. Graphs of λ versus sin ? were plotted for both the first order and second order spectra and then the slope of each of the lines determined. The averaged value of the spacing, d, of each of the lines on the diffraction grating was then determined and an estimate of the error incurred determined.

Results

Prism Spectrometer Experiment

colour	Deviation angle (degree)	Lemda (nm)
Red	133.9	614.8
orange	133.5	589.5
green	133	568.6
Dark green	132	498
light blue	131.5	466.6
violet	130.4	442.1

Table 1: Sodium calibration results

	Diffraction grating
colour	deviation angle (sintheta)	lemda (nm)
violet	0.282	442.1
light blue	0.3	466.6
Dark green	0.312	498
lime green	0.344	515
orange	0.357	588.9
red	0.371	614.8

Table 2: Diffraction Grating results

Figure 3: Diffraction Grating plot

Discussion and Conclusion

The prism spectrum that was obtained for the sodium lamp that could be seen with the resolution of the prism was provided as shown in the table from top to bottom. The measured angles i.e. 2A= and thus the angle of the prismA= (Vaughan 2017). The behavior of the dispersion curve was observed that there is no rapid fall over the range of the wavelengths thus it can be concluded that there is no heavy sloping line meaning that the dispersion of the different spectral lines do not vary so much from each other which is illustrated by the closeness of the refractive index of the provided wavelength range.

For the calibration curve, it is almost a straight line illustrating that the impact of the wavelength of the Angle of Minimum Deviation tends to being linear (Vaughan 2017). This curve can be used in establishing the wavelength of the spectral line that has an unknown wavelength but the Angle of Minimum Deviation is determined using the very apparatus. The aims and objectives of this experiment were thus met with the results illustrating high correlation with the theoretical values as recorded in literature. 

References

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Piascik, A. S., Steele, I. A., Bates, S. D., Mottram, C. J., Smith, R. J., Barnsley, R. M., & Bolton, B. (2014, July). SPRAT: spectrograph for the rapid acquisition of transients. In Ground-based and Airborne Instrumentation for Astronomy V(Vol. 9147, p. 91478H). International Society for Optics and Photonics

Squires, A. D., Constable, E., & Lewis, R. A. (2015). 3D printed terahertz diffraction gratings and lenses. Journal of Infrared, Millimeter, and Terahertz Waves, 36(1), 72-80

Vaughan, M. (2017). The Fabry-Perot interferometer: history, theory, practice and applications. Routledge