1PHY2OPT

Dispersion of a Glass PrismTyler Ritchie 17728183The dispersion of light emitted from a Mercury and a Sodium lamp through a glass prism was investigated using Snells law and Cauchys equation. It was determined that the small prism is constructed out of fused silica, and the larger prism is constructed from corning pyrex 7740. I. INTRODUCTIONDispersion is the phenomenon of polychromatic electromagnetic radiation passing into a dispersive prism of different refractive index from previous media (such as a triangular prism) and the radiation is decomposed into its spectral components. This is due to the change of the angle of refraction of different EM radiation wavelengths, which results in a spectrum when passed through a dispersive prism; in this case a triangular prism is used (Korff, S., 1932).Isaac Newton was one of the first to observe this phenomenon and he then extensively studied the splitting of white light into different wavelengths using a glass prism. Newtons explanation was that light sped up in the prism, later it was proven that light slows down when entering a medium compared to in a vacuum (Born, M., & Emil, W., 1999).

In 1814, Joseph von Fraunhofer observed that in the spectrum of light from the sun, there were dark lines; a lot of research was invested in this by multiple groups, and was found that different substances produce different dispersion spectrums (Korff, S., 1932; Born, M., & Emil, W., 1999).

Snells law describes how light that passes through a glass prism of refractive index n will be deflected, for this experiment, there are three angles that are relevant; refracting angle A of the prism, angle of incidence i1, and the deviation angle D. There is a minimum deviation angle of D, and for this angle there is an i1, which fits equation 1(Latrobe LMS);sin[(A+D)/2] = n*sin(A/2)(1)Refractive index of a prism is wavelength dependent, which is described by Cauchys equation (Latrobe LMS);

n = P + Q/2 + R/4 + (2) P, Q, R are all constants Figure 1 illustrates equation 1;

II. METHODThe experiment was set up as pictured below in figure 2.

First, the mercury discharge lamp was placed in front of the collimator, and the collimator slit was adjusted to ensure a sufficient amount of light was passing into the prism, and the telescope was adjusted to focus the light. The large prism was used first, and a flat edge was placed parallel to the lines on the stage.

The telescope was set at 180 degrees from the collimator, light was seen to pass straight through the prism and this angle was recorded as the reference angle.

Next, the spectral lines of the refracted beam were found, and the angle of each line was recorded. This process was repeated with the small prism and the sodium discharge lamp (Latrobe LMS).III. RESULTS

IV. DISCUSSION

In most cases, it is sufficient to use just two coefficients for Cauchys equation, as this will describe the system with adequate accuracy. Cauchys equation is only applicable for the visible section of the EM spectrum, when normal dispersion occurs, it is a mathematical simplification.

If a higher level of accuracy was required, a variation of Cauchys equation, called the Sellmeier equation can be utilised which covers majority of the EM spectrum (Born, M., & Emil, W., 1999).

It is clear from figure 6 that the large prism has a higher wavelength dependence compared to the small prism.

From the experimental results, it is speculated that the small prism is constructed out of fused silica, and the larger prism is constructed from corning pyrex 7740.

V. CONCLUSIONSDispersion of light in a glass prism was successfully investigated utilising Cauchys equation and Snells law. It was determined that the small prism is constructed out of fused silica, and the larger prism is constructed from corning pyrex 7740.References

Latrobe LMS, Prism Spectroscopy: Extended Student Guide, retrieved on 29/03/2015 from file:///C:/Users/Tyler/Downloads/Prism%20-%20Extended%20Student%20Guide%20(2).pdf Korff, S. (1932). Optical Dispersion. Reviews of Modern Physics, 4(3), 471-503.

Born, M., & Emil, W. (1999). Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Principles of Optics, 7, 14-24Figure 4. Calculation of Refractive Indecies.

Figure 1. Refraction by a prism showing angle of incidence, refracting angle, and angle of deviation. (Latrobe LMS)

Figure 2. Experimental set-up.

Figure 3. Refracting Angle Measurements.

Figure 5. P and Q Values for Cauchys Equation

Figure 6. Graph of Refractive Index vs Wavelength