Theory of the Prism Spectrometer Experiment

Theory of the optical optical prism Spectrometer ExperimentIntroductionWhen a beam of aerial is catching from air to glass, the irradiation is bent according to Snells lawsin0air= nsin0glassWhere the slants are calculated from the surface normal (the withdraw perp give upicular to the surface) and n is the prop nonpareilnt of digression of the glass. The power of digression is a dimension-less number and is a musical rhythm of how powerfully the medium b devastations shadowy. The greater n is, the more the light is bent. The index of refraction of air is 1. For glass, n varies from 1.3 to 1.8, depending on the type of glass and on the wavelength of the light.White light is made up of all the colors of the rainbow scarlet, yellow, thou, blue, and violet. distinguish up to(p) colors correspond to different wavelengths. Human eyes are peeled to light with wavelengths in the range 390 nm (violet) to 750 nm (red) (1 nm = nanometer = 10-9 m).Range of human visionGlass ha s a greater index of refraction at shorter wavelengths, that is, it bends blue light more than red light. So a prism chiffonier be pulmonary tuberculosisd to deal white light into its part colors.Blue red wavelengthIn this experiment, we run out use a prism spectrometer to measure the dispersion angle of various wavelengths. From the measurements, we go away make a graph of the index of refraction vs. wavelength. The form of the curve of index of refraction as a serve of wavelength, k nown as the Cauchy formula, isn = A + B/l2 Or n = A + (b/l)2As a light source, we leave use a mercury lamp, which emits light at several discrete wavelengths. The device we are use is called a prism spectrometer because, once the prism is calibrated, it washbasin be used to measure the wavelengths of the songs in the spectra produced by various atoms. The spectra turn out bright lines at event wavelengths, which correspond to light emitted during the transition mingled with different ene rgy states of the atoms. You elate distinct lines because the atoms exist only in distinct, quantized energy states. Trying to explain the data from such experiments the earthly concern and pattern of sharp ghostly linesled to the development of quantum mechanics.When a re of light is refracted by a prism, the angle between the incoming and outstrip rays is called the angle of deviation (b). For a presumption prism and a given wavelength, the value of b depends on the angle between the incoming ray and the surface of the prism. b is minimum when the angles of the incoming and outgoing rays make pit angles with the prism surfaces. In this special symmetric case, the prisms index of refraction (n) is link to b and the apex angle of the prismN= The prisms that we will use all countenance a = 60 (exactly, we assume).There exist extensive slackens of the line spectra of many elements. In the branch part of the experiment, you will be using the known spectrum of mercury to cali brate your prism spectrometer. As a result, you score measured the curve of index of refraction as a give way of wavelength. So if you measure a new line of a spectrum, you sens calculate the index of refraction and use your curve to vista up the wavelength for the new line. This process is used in identifying the elements present in alien samples, such as the atmospheres of distant stars. The element helium, now used to aggrandize birthday balloons, was first discovered by observing the atmosphere of a nearby the star, the sun (helios is Greek for sun). In the last part of the experiment you will stick the opportunity to measure the spectrum of a gas in this fashion.The fine prism spectrometers used in this lab were purchased in 1970 for $700 each. today inferior models are available for $1700. Handle them with respect Never troops any partsOBJECTIVESLearn the theory of the prism spectrometer, and be able to explain the functions of its various comp ints.Observe the spectr um of a mercury discharge lamp and picture the angle of deviation for the spectral lines.Determine the index of refraction of a glass prism for various wavelengths.Use the calibrated prism to measure unknown wavelengths.Observe color sensation caused by light of particular wavelengths.Methodology1. Become familiar with the spectrometera) Identify each component the sick tabularise, the prism table, the collimator, and the mashb) discover the clamping screws and the fine alteration screws for the compass and the black table. Note the clamping screw for the prism table.c) Note how to adjust the squeeze stress and the eyepiece.d) Note how to adjust the mother fucker riveting in the collimator tube. Note how the cuckoo width stool be adjusted and how the cut predilection can be scatterd.2. Practice reading the angle from a skillful protractor outstrip on the rim of the black table. Use the Vernier scale with the little magnifying glass to read the angle to the nearest a rc minute.3. organize the spectrometerIn order to correctly measure angles with the spectrometer, we must first aline it. To do so, use the following stepsa) Telescope focus Do non put the prism onto the cash table yet. That will come later.Notice that in that location are two knobs associated with the squash. They are located directly under the telescope place. One points along the barrel and one is perpendicular to it. The knob that is along the barrel will lock the telescopes position and will prevent it from rotating. When it is locked guttle in this way, you can use the other knob for a fine adjustment, to boot out it by precise small amounts. If the telescope is non unlocked, turn the knob that is pair to the barrel counterclockwise until you can freely rotate the telescope.Turn the telescope so that it is not pointing at the collimator unless is instead aimed at something as far away from you in the room as possible. now rotate the focus adjustment(See diagram on page 5) until you can see through the telescope clearly. You whitethorn notice that the image is upside down. This is normal. alone ensure that it is as clear and in focus as you can. afterwards this adjustment, you should not adjust the focus of the telescope again.b) Telescope alignment today place a white light (desk lamp) in front of the tear on the end of the collimator (in the diagram on page 5, the desk lamp goes where the HG lamp is pictured). straight off rotate the telescope until it is pointed at the collimator. You should imagine a straight line going from the lamp through the collimator, and through the telescope. By looking through the telescope, you should be able to line up the crosshair with the slit in the far end of the collimator. By locking down the telescope and using the fine adjustment (the knob perpendicular to the one that you used to lock down the telescope) you should be able to do this rattling accurately. If you are unable to see the slit, it may be closed too tightly.You can widen and narrow the slit by rotating the adjuster on the collimator (it is located on the far end of the collimator, much interchangeable the focus for the telescope). This will adjust the slit width, but will not focus the slit. If the slit does not have truly crisp edges when you look through the telescope, collide with the end of the collimator near the lamp in and out to focus it. If your slit is not vertical in the telescope, you can also rotate it so that it is. Once you have a expert thin, well-focused slit, with your crosshairs centered on it and your telescope locked down, you are now ready to align the scales to read the angle.c) Angle adjustment If you look below the set of knobs that ascendance the telescope, you will see another pair of knobs that look identical to the ones for the telescope. These knobs perform the analogous functions (locking down and fine adjustment) for the black table itself. If you unlock the black table, you can rotate it. Notice that there are two windows in which you can read an angle. We desire to rotate the table until one of the windows has 0 (zero) lined up with 0 (zero) or 360 (since a circle is 360 degrees, 360 is the same as 180. If at all possible, we should try to use set it so that this window is to the left-hand(a) of the telescope (as we are looking over the barrel toward the lamp) because this will make reading our angle easiest. (Please have a look at the diagram on page 5) On some scopes there is a small magnifier attached to the black table over one window, and this would also be advantageous to use. Once you have aligned them, you will lock down the black table and will not rotate it again. From now on, we will only rotate the telescope.d) Prism placement straightaway you should place the prism in the center of the silver table. Recall that light is bent toward the base of the prism, so it should be placed on the silver table so that the gray plastic part make s a C shape if you were to look at it from the telescope side of the apparatus. Now, without moving the telescope, cue your head to the left (about to where the telescope is rotated to in the diagram on page 5) and look into the prism. You will have to put your head down at the height of the telescope/collimator. Now rotate the silver table clockwise until you can see a nice rainbow like spectrum inside the prism.(You should notice that the rainbow is inside of a black circle. You are seeing the light coming out of the collimator and bent through the prism.) If it does not look like a very nice, bright, well-formed rainbow, you probably do not have your head in the right place move further left and try to rotate the silver table rearwards and forth. Once you have found it, unlock the telescope (not the black table) and rotate it to the left where you were looking. Now look through the telescope, and you should be able to find the rainbow. We are now in about the right place to fin d our spectrum with the mercury drying up lamp and to adjust for the minimum angle of deviation.e) Minimum angle of deviation Now, leave off the white light and replace it with the mercury vapor lamp. You will want to move the lamp until it is aligned with the slit. To do this, look through the telescope and move the lamp back and forth until it is nice and bright in the telescope. Instead of a complete rainbow, you should now see only certain bands of color. If your bands do not look nice and sharp, you may have to adjust your slit focus or width. Some lines are better seen if you tighten the slit. (The lamp should be very close to the slit.) Move the telescope back and forth until you hit the crosshair lined up on the green band. Now look back to the diagram on page 5. We want to make the angle b as small as possible. To do this, rotate the silver table back and forth just a little telephone number. You should be able to get the green line to move to the right. Now realign the crosshair on the green line and rotate the silver table a little bit again. Then realign the crosshair on the green line. You should go back this process until no matter which way you rotate the silver table, the green line goes to the left, not the right. When this occurs, and the green line is as far as you can get it to go to the right, you are at the minimum angle of deviation. This angle should be around 51 or 52 degrees for the green line. If it is not, you may not have aligned the scales correctly, please repeat steps c, d, and e from above. (Record it below). every time that you do a different color, you will have to repeat this process.f) Record the prism number and read the deviation angle on the protractor.Prism _______ b = _______ _______ = ___________4. Measure the angle of deviation for each of the spectral lines of the Mercury lamp. The wavelengths and colors of the spectral lines are given in the table below. While making measurements, unclamp and rotate the pri sm table to check that the prism is oriented for minimum angle of deviation for the red, green, and blue lines.When measuring very closely spaced lines, like the double yellow lines, make the slit very narrow and check the focus. When measuring dim lines, make the slit wider.