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If time permits, use the simulation software provided to compare your value of the slit separation with that predicted by the program. 
1. Choose Applications of Interference and Diffraction from the menu.
2. Choose Gratings from the menu at the top of the screen.
3. Choose the Transmission Grating - Spectrum option from the pull-down menu.
4. Enter the wavelengths of two of the lines you have measured, a slit width of 0.0001 mm and the slit separation you determined.
5. Compare the predicted angular positions of the lines with the values you measured. Comment on the result.
6. Investigate the effect of changing the slit width, slit separation or wavelength of the radiation.

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

Duarte, F. J. (2015). Tunable laser optics. CRC Press

Guanter, L., Kaufmann, H., Segl, K., Foerster, S., Rogass, C., Chabrillat, S., ... & Straif, C. (2015). The EnMAP spaceborne imaging spectroscopy mission for earth observation. Remote Sensing, 7(7), 8830-8857

Hadni, A. (2016). Essentials of Modern Physics Applied to the Study of the Infrared: International Series of Monographs in Infrared Science and Technology (Vol. 2). Elsevier

Hartmann, N., Helml, W., Galler, A., Bionta, M. R., Grünert, J., Molodtsov, S. L., ... & Bostedt, C. (2014). Sub-femtosecond precision measurement of relative X-ray arrival time for free-electron lasers. Nature photonics, 8(9), 706

Hossain, M. A., Canning, J., Ast, S., Cook, K., Rutledge, P. J., & Jamalipour, A. (2015). Combined “dual” absorption and fluorescence smartphone spectrometers. Optics letters, 40(8), 1737-1740

Leedle, K. J., Pease, R. F., Byer, R. L., & Harris, J. S. (2015). Laser acceleration and deflection of 96.3 keV electrons with a silicon dielectric structure. Optica, 2(2), 158-161

Mouroulis, P., Van Gorp, B., Green, R. O., Dierssen, H., Wilson, D. W., Eastwood, M., ... & Loya, F. (2014). Portable Remote Imaging Spectrometer coastal ocean sensor: design, characteristics, and first flight results. Applied optics, 53(7), 1363-1380

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

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