Determination of Refractive Index of Prism Using Spectrometer and Various Light Sources
Determination of Refractive Index of Prism using Spectrometer and Various Light Sources Dimain, Marion; Gonzales, Jade; Pancho Jr., Ronel; Viloria, Matthew David College of Engineering, University of the Philippines, Diliman, Quezon City 1101, Philippines [email protected] [email protected]
com [email protected] com tewhmat. [email protected] com Abstract The study aims to measure the refractive index of a triangular prism using a spectrometer, utilizing different gas discharge tubes as light source.
With the use of the discrete spectrum of mercury vapor, hydrogen gas and neon gas, each of the visible color in their respective spectrum passing through the prism was used as the incident ray. The results determined that the red light of the neon discharge tube brought about a calculated refractive index closest to the theoretical value. I. Introduction The spectrometer is an instrument for analyzing the spectra of radiations. A prism refracts the light into a single spectrum, whereas the diffraction grating divides the available light into several spectra.
Because of this, slit images formed using a prism are generally brighter than those formed using a grating. Spectral lines that are too dim to be seen with a grating can often be seen using a prism. Unfortunately, the increased brightness of the spectral lines is offset by a decreased resolution, since the prism doesn’t separate the different lines as effectively as the grating. However, the brighter lines allow a narrow slit width to be used, which partially compensates for the reduced resolution. Prism refers to any transparent medium having two or more plane surfaces.
A familiar example is the triangular prism, usually made of glass, used to split beam of white light into its component colors. When light is refracted through a prism it is dispersed into its constituent colors, and the angle at which the light emerges from the prism depends upon its wavelength. A prism spectrometer can be used to measure the deviation angles. Since the deviation angles also depend upon the index of refraction of the glass from which the prism is made, they can be used to calculate the index of refraction ? at the different wavelengths via: ? sinA+Dmin2sinA2 (1) where A is the apex angle of the prism and Dmin is the minimum deviation angle of a specific color in the discrete spectrum.  The tip of the prism where the two refracting surfaces meet is the apex angle. Deviation angle is defined as the angle between the original incident beam and the final transmitted beam. Figure 1. The apex angle A and the deviation angle D.  With reference to Figure 1, light travelling in medium n1 is incident at an angle ? i1 to the normal of one face of the prism having refractive index n2.
The incident light is refracted at the first interface and travels at angle ? t1 with respect to the normal. This light is incident at the second face of the prism at an angle ? i2 and finally refracted again to exit the prism at angle ? t2. The deviation angle is therefore equal to: D=(? i1 – ? t1) + (? t2-? i2) (2) In Figure 1, the polygon abcd, there are two right angles ? abc and ? adc. Also for the polygon, since the sum of opposite angles should be 180? so ? bcd + ? A = 180?.  Further, in triangle bcd we have ? bcd+? 1+ ? i2=180?. Therefore, the sum of angle A is ? t1+? i2. Relating D and A, D=? i1+ ? t2- ? A. When the prism is rotated perpendicular to the plane of incidence, i. e. such that the incidence angle ? i1 is varied continuously, the deviation of the transmitted light changes.  This deviation goes through a minimum Dmin. By symmetry we can argue that the minimum deviation position should be independent of the direction in which light enters the prism. In other words, light entering the prism from the left or right should exhibit the same properties of refraction, minimum deviation, etc. 5] Therefore, if we reverse the direction of light, thus having the new incident light ? i1new=? t2old and ? t2new=? i1old. Experimentally, it is observed that Dmin occurs when the refracted ray inside the prism makes equal angles with the two faces. This means that if we reverse the direction in which light is incident on the prism, we have a new ? i1= ? t2at which the Dmin occurs. However, experimentally, only one Dmin occurs and therefore ? i1= ? t2 at Dmin.  Using Snell’s law, we have: n1n2=sin? i1sin? t1 (3) Using minimum deviation we have:
Dmin=2sin? i1-A or ? i1=Dmin+A2 (4) From the equivalent sum of angle A, ? t1=A-? i2. Thus, using the minimum angle condition we have ? t1=A2. Substituting the values of ? i1 and ? t1 with n2 as one on Equation 3, yields Equation 1. II. Methodology The materials utilized in the study were triangular prism of unknown refractive index, laser light source, protractor, gas discharge tubes (mercury, hydrogen, and neon), high voltage power supply for discharge tubes and spectrometer.
The index of refraction of the prism was first measured using the protractor, laser light source and prism. First the telescope was focused to distant objects i. e. infinity and maintained until the experiment is over, so as not to refocus again.  The collimator was adjusted such that the image seen in the telescope is sharp.  The diffraction grating holder from the spectrometer table was removed and replaced with prism clamp. The triangular prism was placed and clipped on the table and oriented as shown in Figure 2.
The telescope was set to read the angle of the light that is reflected off each face of the prism. The difference between the scale readings at clockwise point a and counterclockwise point b, shown in the Figure 2, equals twice the apex angle A. The value of the apex angle A was calculated. Figure 2. The experimental set-up and measurement of the apex angle A.  Using the positioning jig, the prism was rotated on the spectrometer table so that it is oriented as shown in Figure 3.When gases or vapors of elements are heated or exposed to high voltage they emit light.
The emitted light can be split into its component wavelengths by passing it through a diffraction grating or prism. The emission spectrum is unique and characteristic to each element. The discrete spectrum each gas discharge tube was observed. The average angular displacements (clockwise and counter-clockwise) of each color were tabulated while rotating the telescope as the visible colors of the spectra was scanned. Using the values gathered for the apex angles and angle of minimum deviation, the index refraction was computed using Equation 1. Figure 3.
Measurement of the angle of minimum deviation D.  III. Results and Discussion The measured apex angle A of the prism was 60?. Using the laser light source the angle of 45? was used as incident angle with respect to the normal line, the emergent ray has a 28?. The calculated refractive index, using Equation 3, was 1. 506175959; this will be treated as the theoretical value. The table below shows the calculated index of refraction using Equation 1. The only visible colors for mercury discharge tube were violet, green and yellow, red and blue-green for hydrogen, and yellow and red for neon.
The visible colors in each spectrum using prism were less compared when using diffraction grating. This can be due to the limited scope observable using triangular prisms as dispersion agent of the spectrometer. There was an increasing trend of indices as minimum deviation angle increases and as the wavelength of the colored light decreases independent of the element contained in the discharge tube. A prism refracts the light into a single spectrum, whereas the diffraction grating divides the available light into several spectra.
Because of this, slit images formed using a prism are generally brighter than those formed using a grating. That is why prisms are preferred when the desired dispersion is weak. Spectral lines that are too dim to be seen with a grating can often be seen using a prism. Unfortunately, the increased brightness of the spectral lines is offset by a decreased resolution, since the prism doesn’t separate the different lines as effectively as the grating. However, the brighter lines allow a narrow slit width to be used, which partially compensates for the reduced resolution.
The lesser number of colors of light seen in the scope of a spectrometer utilizing a prism as a dispersion medium can also be associated to the unseparated spectral lines of the discharge tubes. The average value of the refractive index closest to the theoretical was given off by the neon discharge tube with 1. 515508062 and 0. 6196% deviation. The color red of neon gave off the refractive index closest to the theoretical with 1. 513609903. It connotes that it is more reliable to use neon discharge than mercury and hydrogen in measuring the index of refraction of a prism.
The experimental design inadequately addressed the hypothesis due to unavailability of materials; further experimentation could be done using other elements and other prism of different refractive indices and apex angles to explore if there will a significant difference with respect to the gathered data. Table 1. Different minimum deviation angles of the spectrum of different discharge tubes. Element| Color| Minimum Deviation Angle D| Index of Refraction ? | Average Index of Refraction ? | Percent Deviation| Mercury| Violet| 41? 30’| 1. 548785288| 1. 540510872| 2. 2796%| | Green| 40? 44’| 1. 540284548| | | | Yellow| 40? 2’| 1. 3246278| | | Hydrogen| Blue-Green| 39? 56’| 1. 53134071| 1. 528902825| 1. 8384%| | Red| 39? 30’| 1. 52646494| | | Neon| Yellow| 38? 42’| 1. 517406221| 1. 515508062| 0. 6196%| | Red| 38? 22’| 1. 513609903| | | IV. Conclusion and Recommendation It is therefore concluded that the refractive index of a prism can be measured using a spectrometer. The most reliable gas discharge tube between hydrogen, mercury and neon to measure refractive indices was neon with 1. 515508062 and 0. 6196 percent deviated from the theoretical value of 1. 506175959. The color red of neon gave off the refractive index closest to the theoretical with 1. 13609903. The visible colors in each spectrum using prism were less compared when using diffraction grating. There was an increasing trend of indices as minimum deviation angle increases and as the wavelength of colored light decreases independent of the element contained in the discharge tube. The experimental design inadequately addressed the hypothesis due to unavailability of materials, further experimentation could be done using other elements and other prism of different refractive indices and apex angles to explore if there will a significant difference with respect to the gathered data.
Acknowledgements First and foremost, the students would like to thank Mrs. Jen-jen Manuel, our physics laboratory instructor, for his patience, guidance and understanding. The National Institute of Physics for letting us conduct this experiment. The staff in-charge-of-the-instruments for letting the students borrow instruments vouched by University of the Philippines I. D. References 1. Young, H. , University Physics, 12th Edition L. P. E. , Chapter 38: Photons: Light Waves Behaving As Particles, Photoelectric Effect, Pearson Education South Asia PTE LTD (2009). 2. Go, Mary Ann, et. l. (Laboratory Manual Authors), Physics 73. 1, Spectral Fingerprinting, The Spectrometer (2007). 3. http://www. cmi. ac. in/~debangshu/lab1/spectrometer. pdf 4. http://uregina. ca/~szymanss/uglabs/p112/Experiments/112-08Spectr08. pdf 5. https://www. google. com. ph/url? sa=t&rct=j&q=&esrc=s&source=web&cd=4&cad=rja&ved=0CEUQFjAD&url=http%3A%2F%2Fphysics. wustl. edu%2Fclassinfo%2F316%2FTheory%2FRefraction. pdf&ei=0I0xUe_iA6i9iAfiooGoBg&usg=AFQjCNEfjICiK9bxd9xT7AZsYZT-j5ybDw&sig2=s9OmxcBtP3WtmnbVM7nlQQ&bvm=bv. 43148975,d. aGc