54 #23 Prism Spectroscopy Objective The overall objective of this experiment is to investigate the dispersive power of a glass prism, and to see how different incandescent gases produce distinctly different spec- tral line patterns. The specific goals are: 1. To determine the wavelengths of several spectral lines of hydrogen 2. To determine the wavelength limits of the visible spectrum 3. To determine the type of glass composing the prism 4. To determine the Cauchy function for the glass prism Introduction and Theory Types of Spectra In 1666, Isaac Newton discovered that when a beam of sunlight is passed through a prism, it is spread out into a number of different directions, each having a different color. this band of varying color is called a spectrum. Spectroscopy is that branch of physical science concerned with the study and analysis of spectra. Although we will confine our study in this experiment to the visible spectrum, the field of spectroscopy deals with the entire electromagnetic spectrum. Figure 23.1 shows the electromagnetic spectrum. All electromagnetic waves travel at the same speed c = 3.0 x 108 m/s in free space, but differ in frequency, wavelength, the sources that produce them, their interaction with materials, and the instruments used to detect and measure them. Light, or the visible spectrum, is defined as that radiation to which the human eye is sensitive. The visible spectrum, as indicated in Fig. 23.1, comprises a relatively small por- tion of the entire electromagnetic spectrum. It extends from 400 nm (violet) to about 700 nm (red), where one nm is equal to 10-'m. Wavelength (m) 1 10-1 10-2 10-3 104 105 106 10-7 10-8 10-9 10-10 10-11 10-12 10-19 10-14 10-15 10-16 108 107 106 105 104 103 102 10 . Long waves Radio waves Infrared Ultraviolet X rays Gamma rays 10 102 103 104 105 106 107 108 109 1010 1011 1012 1013 1011 1015 1016 1017 1018 1019 1020 102 1022 1023 1024 Frequency (Hz) - Fig 23.1. The electromagnetic spectrum. There are three main types of spectra: continuous, emission-line, and absorption-line. A continuous spectrum is produced by light from an incandescent solid or liquid: it contains a continuous gradation of colors (wavelengths), from red at one end to violet at the other. 55 noen An emission-line (also called bright-line) spectrum is produced by exciting an element in the gaseous state by means of an electric discharge or by heating. Such a spectrum con- sists of bright lines, corresponding to light of definite colors (wavelengths), separated by dark spaces. The number and relative positions of the lines depend on the element used and the specific method of excitation. An absorption spectrum is produced when light from a source radiating a continuous spectrum is passed through some cooler absorbing medium. The resulting spectrum is crossed by dark spaces or lines which form the absorp- tion spectrum of the absorbing medium. Spectrum analysis is the decomposition of a beam of light into its constituent wave- lengths and the examination of the image so formed. A spectroscope is an optical instru- ment for producing and analyzing spectra. When a beam of light is passed through a spec- troscope, it is separated, or dispersed, into a spectrum. Those wavelengths of radiation which are contained in the beam will show up as distinct colors in the spectrum. If, on the other hand, a certain wavelength or range of wavelengths of radiation is not present in the incoming beam, then dark spaces will appear in the spectrum at positions corresponding to where those colors would be seen had they been present in the beam. Each chemical element has a unique atomic structure which determines the wave- lengths and intensities of the spectral lines it emits when the atoms are excited by, for ex- ample, heating. Consequently, the light which is emitted by such an incandescent object contains an encoded message of the chemicals which compose it. The spectroscope de- codes the message by spreading the light into its spectrum. Thus, each element can be said to produce its own characteristic spectral “fingerprint.” This fact has enabled astronomers to determine the chemical compositions of the Sun and distant stars without ever leaving Earth! The Components of a Spectroscope The original spectroscope used by Newton was a prism spectroscope. When a beam of light is passed through a glass prism, it is refracted or deviated from its original direc- tion, and also dispersed into a spectrum. Dispersion occurs because the velocity of light in the prism depends on the wavelength of the light: hence the index of refraction, n (=c/v), is different for each wavelength, and the angle of deviation is also different. The simple prism spectroscope is shown in Fig. 23.2. It consists of three essential parts: a collimator, a dispersing element (the prism), and a telescope. (Each of these parts will be discussed in somewhat more detail in Experiment #24.) The collimator is a tube with a converging lens at one end and a find slit of adjustable width placed in the focal plane of the lens at the other end of the tube. The function of the collimator lens is to ren- der the rays of light from the slit parallel. the prism bends and disperses the rays of light into a spectrum. The telescope consists of the objective lens, which brings the parallel rays of light to a focus in its focal plane, and the eyepiece, through which the image of the spectrum is viewed. If the light is monochromatic (i.e., of a single wavelength) a single image of the slit appears. If a polychromatic source (i.e., one containing several different wavelengths) is used, several images of different color will appear side by side in certain positions, each being an image of the slit formed by one component wavelength of the light. The position of each image can be measured from the setting of the telescope as indicated on the vernier scale of the spectroscope. JU 虫 PRISM CLAMP 日く UGHT SOURCE PRISM Fig. 23.2. Schematic of a simple prism spectroscope The Angle of Minimum Deviation The deviation of a beam of light by a prism also depends on the angle of incidence. It is found that the deviation of light emerging from a prism is a minimum for that unique angle of incidence which results in the beam passing through the prism parallel to its base (Fig. 23.3). α ө Fig. 23.3. The angle of minimum deviation for a prism. 57 The deviation angle is greater for all other angles of incidence. It can be shown that the index of refraction of a prism for light of wavelength 2 is related to the angle of mini- mum deviation, 0, by the following expression: sin((a + 0)/2] (23.1) sin(a/2) N = where a is the apex angle, and 8, is defined as shown in Fig. 23.3. As a result, the index of refraction for a glass prism can be determined by measuring a and e, and since the index of refraction depends on the wavelength of the light used the index of refraction can be measured as a function of wavelength. 1.7 n Silicate Flint 1.6 Borate Flint Quartz Silicate Crown 1.5 Fused Quartz 1.4 400 450 500 550 700 2 (nm) 650 600 SOMO Fig. 23.4. n versus à for different glasses. The Cauchy Function It is found empirically that the index of refraction, n, depends on wavelength, a, in the following manner: あっ +b. (23.2) 22 a n = Equation 23.2 is called the Cauchy function; it closely describes the behavior of n with 2 for glasses where the wavelength is restricted to the visible spectrum. Figure 23.4 shows n versus 2 for several kinds of glass. The constants a and b in the Cauchy function can be determined once experimental data have been obtained for n at several different wavelengths. The simplest way to do this is to define a new variable u= 22, so that Eq. 23.2 becomes n = a + b (23.3) Thus, a plot of the index of refraction n as a function of the quantity u should yield a straight line with slope a and y-intercept b. 58 The Calibration Curve for a Prism Spectroscope A glass prism refracts light into a single spectrum, whereas a diffraction grating di- vides the available light into several different spectra called orders. (Diffraction spectros- copy will be treated in Experiment #25.) Consequently, 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 decrease in resolution, since refraction within the prism does not separate the different lines as effectively as diffraction in the grating. On the other hand, the brighter lines allow a narrow slit width to be used, which partially compensates for the reduced resolution. With a diffraction grating, the sine of the angle of refraction is directly proportional to the wavelength of light (see Eq. 24.1 in Experiment #24). This simple relation does not hold, however, with a prism. In order to measure wavelengths using a prism, a calibration curve, which is a graph of wavelength versus angle of refraction, must be constructed us- ing a light source with a known spectrum. The wavelengths of unknown spectral lines can then be interpolated from the graph. Once a calibration graph is created for the prism, future wavelength determinations are valid only if they are made with the prism aligned precisely as it was when the graph was produced. To ensure that this alignment can be reproduced, all measurements are made with the prism aligned so that the light is refracted at the angle of minimum devia- tion, discussed earlier. Apparatus Check that you have the following equipment on you lab table: - PASCO Model SP-9268 spectrometer - large glass prism (apex angle A = 60°) magnifier for reading vernier scale high-voltage power supply several gas discharge tubes. one incandescent lamp Experimental Procedure A helium gas tube and mercury vapor tube will be used to provide a series of well established wavelength lines (see Table 23.1 and Fig. 23.5) so that the index of refraction can be measured as a function of wavelength using Eq. 23.1. - -
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