3.1SPECTRA White light is a mixture of all wavelengths. When white light is sent through a prism or adiffraction grating it is broken up into a continuous distribution of colors called a spectrum. Therelation between wavelength and color is given in the following table. color wavelength (nm)violet 400 - 450blue 450 - 480blue-green 480 - 510green 510 - 550yellow-green 550 - 570yellow 570 - 590orange 590 - 630red above 630A rainbow is a spectrum produced when sunlight is refracted through raindrops. Any thin slice ofcolor in a continuous spectrum is called a spectrally pure color and is characterized by itswavelength . Spectrally pure colors are rare in most of our natural environment but they areeasily produced in the laboratory. When an electric current is sent through a diffuse transparent gas the gas is heated and glows. Ifthe light from such a gas is passed through a prism or diffraction grating, a discrete set of brightcolors will typically be seen. When a diffraction grating is used the colors appear to be narrowlines parallel to the slits of the grating and are called spectral lines. A collection of these lines(usually in the form of a table or graph) for a gas composed of a given chemical element is calledthe line spectrum of the element.A very different sort of spectrum is produced by a hot opaque object like a lightbulb filament.Instead of discrete spectral lines this incandescent light source produces a broad distribution ofcolors. Every color in the visible range is represented in such a spectrum and the relativeintensities of various colors depends on the temperature of the hot object.3.2Experiment 1: Grating SpectroscopeApparatus: CENCO grating spectroscope, variac-controlled light bulb, sodium andmercury vapor lamps.Procedure: Hold the device so that its right angle is on your left. View through thegrating fixed to the aperture at the short end. Illuminate the vertical slit on the left withthe light to be studied. The nominal wavelength is read on the scale to the right of theslit.A. The spectroscope is not accurately calibrated; the nominal wavelength appearing onthe scale is not the true wavelength. Use the fluorescent lights in the room to make atable of true vs. nominal wavelengthThe actual wavelengths, in nm, are:violet blue green orange red 436 489 545 585 612Compare to the observed lines. Make a table of corrections to be used for subsequentmeasurements.B. Use the spectroscope to find the wavelengths of light from sodium and mercuryvapor lamps. C. Examine the light from the filament of an unfrosted light bulb. Begin by turning thecurrent up to a significant value but not so high that its light is painful. Use thespectroscope to compare the intensity of the violet light to that of the red light. As thecurrent is turned down, all intensities decrease. Can you see a relative difference in theintensity of the violet light compared to the red light? Which color’s intensity decreasesfastest as the current is turned down? Repeat a few times to make sure of your result.D. Take the instrument home for a day or two. Look at and report your findings for lightfrom: a gas flame, a candle flame, automobile headlights, a room lamp, commercialneon lights and the sun at midday and at sunrise or sunset (of course you should notuse light directly from the disk of the sun).3.3Experiment 2 : Prism SpectrometerApparatus: Prism spectrometer, mercury and sodium vapor lamps, hydrogen dischargetube, helium-neon laser The prism spectrometer consists of an equilateral flint prism fixed to a stand containingan adjustable slit, an objective lens that focuses the light from the slit onto the prism,and a telescope consisting of an objective lens and an adjustable ocular with built-incross-hair. The telescope sits on a platform that is free to rotate about a vertical axisthrough the prism. Gross rotation angle of the telescope is changed by moving thetelescope support with the hand while fine adjustments are made with a screw on theright side of the support. Angle of the telescope is measured on a principal scale and ona vernier scale equipped with a viewing lens to read minutes of arc.Procedure: A. Calibration of AnglesLight enters the device through the slit. A typical experiment consists of measuring theangular positions of spectral lines produced when light has gone through the prism.This light emerges as colored images of the slit. The slit should first be openedrelatively wide and placed so as to view the light from a mercury vapor lamp. The linespectra can be located by gross rotation of the telescope housing. Then close down theslit until only narrow spectral lines remain. These will often be slightly curved, forming abow rather than a straight line. Use the fine adjust to line up the vertical cross-hair withthe center of the bow of each spectral line. There will be a dim line far in the violet(404.7nm), a bright violet line (435.8nm), green (546.1nm), and a yellow doublet(577.0nm and 579.1nm). Make a table of the angular position of the telescope for eachof these lines. The yellow doublet lines are so close together that, unless you feelconfident that you have resolved them into two separate lines, it is better to regard themas a single line at the average wavelength. The work should be done by at least twostudents and the results averaged. Then do the same with a hydrogen discharge tube,recording the position of the bright red line (656.3nm) and the blue line (486.1nm).B. Mathematical Description of the CalibationYou now have six spectral lines that span most of the visible spectrum. Use thepointplot function in MAPLE to graph this data and re-measure any points that look likethey do not lie on a smooth curve. To use the prism spectrometer to measure the wavelength of unknown lines it isnecessary to fit the data to a formula. Use the least squares fit command in MAPLE tofit the wavelengths to a polynomial in the angles. It is first necessary to convert todecimal angles. It is suggested that instead of demanding a fit directly to the angle,which is often a large number of degrees that varies only slightly over the visible range,you first subtract from all angles the angular position of the green line. Then yourangular positions will be small positive and negative numbers. The fit will benefit greatlyin accuracy from this procedure. When using your formula you will have to remember to3.4always make this change