Determination of Refractive Index of Prism Using Spectrometer and Various Light Sources

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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

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 μ at the different wavelengths via: μ=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.[3] 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.[5]
With reference to Figure 1, light travelling in medium n1 is incident at an angle θi1 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 θt1 with respect to the normal. This light is incident at the second face of the prism at an angle θi2 and finally refracted again to exit the prism at angle θt2. The deviation angle is therefore equal to: D=(θi1 - θt1) + (θt2-θi2) (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˚.[5] Further, in triangle bcd we have ∠bcd+θt1+ θi2=180˚. Therefore, the sum of angle A is θt1+θi2. Relating D and A, D=θi1+ θt2- ∠A. When the prism is rotated perpendicular to the plane of incidence, i.e. such that the incidence angle θi1 is varied continuously, the deviation of the transmitted light changes. [5] 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...
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