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# Theory of the Prism Spectrometer - Experiment

Introduction

When a laser beam is sent from air to wine glass, the ray is bent according to Snell's law

sin0air= nsin0glass

Where the angles are assessed from the top normal (the lines perpendicular to the surface) and n is the index of refraction of the a glass. The index of refraction is a dimension-less number and is also a way of measuring how highly the medium bends light. The greater n is, a lot more the light is bent. The index of refraction of air is 1. For wine glass, n varies from 1. 3 to 1 1. 8, depending on type of goblet and on the wavelength of the light.

White light is made up of all the colors of the rainbow - red, yellow, renewable, blue, and violet. Different colors match different wavelengths. Human being eyes are very sensitive to light with wavelengths in the number 390 nm (violet) to 750 nm (red) (1 nm = nanometer = 10-9 m).

Range of human being vision

Glass has a larger index of refraction at shorter wavelengths, that is, it bends blue light more than red light. So a prism may be used to disperse white light into its component colors.

Blue red wavelength

In this experiment, we will use a prism spectrometer to measure the dispersion angle of varied wavelengths. In the measurements, we can make a graph of the index of refraction vs. wavelength. The form of the curve of index of refraction as a function of wavelength, known as the Cauchy method, is

n = A + B/l2 Or n = A + (b/l)2

As a source of light, we use a mercury light fixture, which emits light at several discrete wavelengths. The device we are employing is named a prism spectrometer because, once the prism is calibrated, it can be used to gauge the wavelengths of the lines in the spectra made by various atoms. The spectra contain bright lines at particular wavelengths, which match light emitted during the move between different energy says of the atoms. The truth is specific lines because the atoms can be found only in particular, quantized energy claims. Trying to explain the data from such experiments- the life and routine of well-defined spectral lines-led to the introduction of quantum mechanics.

When a ray of light is refracted by way of a prism, the viewpoint between the inbound and outgoing rays is named the position of deviation (b). For confirmed prism and confirmed wavelength, the value of b will depend on the angle between your inbound ray and the surface of the prism. b is minimum when the angles of the incoming and outgoing rays make identical perspectives with the prism surfaces. With this special symmetric circumstance, the prism's index of refraction (n) relates to b and the apex position of the prism

N=

The prisms that people will use all have a = 60 (exactly, we believe). There exist extensive dining tables of the collection spectra of several elements. Inside the first part of the experiment, you'll be using the known spectral range of mercury to calibrate your prism spectrometer. Because of this, you have assessed the curve of index of refraction as a function of wavelength. So if you measure a new line of a spectrum, you can determine the index of refraction and use your curve to research the wavelength for the new line. This process is utilized in determining the elements within unknown samples, including the atmospheres of distant stars. The element helium, now used to fill birthday balloons, was first discovered by observing the atmosphere of the nearby the star, the sun (helios is Greek for sun). Within the last part of the experiment you should have the chance to measure the spectral range of a gas in this fashion.

The fine prism spectrometers used in this laboratory were purchased in 1970 for \$700 each. Today inferior models are for sale to \$1700. Deal with them with admiration! Never pressure any parts!Ж

OBJECTIVES:

1. Learn the idea of the prism spectrometer, and be able to explain the functions of its various components.
2. Observe the spectral range of a mercury discharge light fixture and record the angle of deviation for the spectral lines.
3. Determine the index of refraction of your goblet prism for various wavelengths.
4. Use the calibrated prism to evaluate unidentified wavelengths.
5. Observe color discomfort brought on by light of particular wavelengths.

Methodology

1. Understand the spectrometer

a) Identify each aspect: the dark-colored stand, the prism stand, the collimator, and the telescope

b) Please note the clamping screws and the fine modification screws for the telescope and the dark table. Take note the clamping screw for the prism table.

c) Be aware how to adapt the telescope concentration and the eyepiece.

d) Please note how to adjust the slit centering in the collimator pipe. Note how the slit width can be altered and the way the slit orientation can be rotated.

2. Practice reading the position from an accurate protractor size on the rim of the black table. Utilize the Vernier range with the little magnifying glass to read the position to the nearest arc minute.

3. Align the spectrometer

In order to effectively measure perspectives with the spectrometer, we must first align it. To take action, use the following steps:

a) Telescope focus: Usually do not place the prism onto the silver precious metal table yet. That may come later.

Notice that we now have two knobs from the telescope. They are located directly under the telescope barrel. One points over the barrel and one is perpendicular to it. The knob that is along the barrel will lock the telescope's position and can prevent it from spinning. When it's locked down in this way, you can use the other knob for a fine adjustment, to turn it by very small amounts. If the telescope is not unlocked, turn the knob that is parallel to the barrel counterclockwise until you can freely rotate the telescope.

Turn the telescope so that it is not directing at the collimator but is instead aimed at something as a long way away from you in the room as is feasible. Now turn the target adjustment

(See diagram on web page 5) until you can view through the telescope obviously. You may notice that the image is upside down. That is normal. Just ensure that it's as clear and in target since you can. After this adjustment, you ought not adjust the concentration of the telescope again.

b) Telescope alignment: Now place a white light (workplace lamp) before the slit on the finish of the collimator (in the diagram on site 5, the desk lamp goes where the "HG lamp fixture" is pictured). Now rotate the telescope until it is pointed at the collimator. You should imagine a right line going from the light 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 off end of the collimator. By locking down the telescope and using the fine adjustment (the knob perpendicular to the the one that you used to lock down the telescope) you ought to be able to do this very accurately. If you're unable to start to see the slit, it might be closed too tightly.

You can broaden and slim the slit by rotating the adjuster on the collimator (it is located on the very good end of the collimator, much like the target for the telescope). This can adapt the slit width, but will not concentrate the slit. In case the slit doesn't have very crisp edges when you look over the telescope, move the end of the collimator near to the lamp fixture in and out to focus it. When your slit is not vertical in the telescope, you can also turn it so that it is. Once you have a nice thin, well-focused slit, with your crosshairs centered on it as well as your telescope locked down, you are now prepared to align the scales to learn the angle.

c) Angle adjustment: In the event that you look below the set of knobs that control the telescope, you will notice another pair of knobs that look similar to people for the telescope. These knobs perform the same functions (locking down and fine modification) for the dark table itself. In the event that you unlock the black desk, you can turn it. Notice that there are two home windows in which you can read an viewpoint. We want to rotate the desk until one of the house windows has 0 (zero) lined up with 0 (zero) or 360 (since a circle is 360 levels, 360 is equivalent to 180. If possible, we should make an effort to use arranged it so that this window is to the left of the telescope (as we are looking within the barrel toward the lamp) because this can make reading our position easiest. (Please take a look at the diagram on site 5) On some scopes there may be a small magnifier mounted on the black desk over one windows, which would also be beneficial to use. Once you have aligned them, you will lock down the black table and can not turn it again. From now on, we will only rotate the telescope.

d) Prism position: Now you should place the prism in the center of the silver table. Recall that light is bent toward the bottom of the prism, so it should be put on the magic table so that the gray clear plastic part makes a "C" form if you were to look at it from the telescope side of the equipment. Now, without moving the telescope, move your head left (going to where the telescope is rotated to in the diagram on page 5) and look in to the prism. You will need to put your head down at the level 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 group. You are discovering the light coming out of the collimator and bent through the prism. ) If it does not look like a very nice, dazzling, well-formed rainbow, you probably do not have your head in the right place; move further eventually left and make an effort to rotate the magic table back and forth. Once you have found it, unlock the telescope (not the black desk) and rotate it left where you were looking. Now look over the telescope, and you should be able to find the rainbow. We are actually in about the right place to find our variety with the mercury vapor light fixture and to modify for the bare minimum position of deviation.

e) Minimum perspective of deviation: Now, remove the white light and replace it with the mercury vapor lamp fixture. You should move the light fixture until it is aligned with the slit. To do this, look through the telescope and move the lamp backwards and forwards until it is nice and shiny in the telescope. Instead of a full rainbow, you should now see only certain rings of color. In case your bands do not look nice and razor-sharp, you might have to adjust your slit target or width. Some lines are better seen if you tighten up the slit. (The light should be very near to the slit. ) Move the telescope backwards and forwards until you get the crosshair prearranged on the renewable band. Now look back to the diagram on site 5. You want to make the angle b as small as possible. To get this done, rotate the metallic table back and forth just a tiny bit. You should be able to receive the green line to move to the right. Now realign the crosshair on the renewable line and rotate the metallic table a bit again. Then realign the crosshair on the renewable line. You need to repeat this process until no matter which way you rotate the silver desk, the green lines goes to the departed, not the right. When this occurs, and the inexperienced line is really as far since you can get it to visit the right, you are at the minimum position of deviation. This angle should be around 51 or 52 diplomas for the green line. If it's not, you might not have aligned the scales effectively, please repeat steps c, d, and e from above. (Record it below). Every time that you execute a different color, you will have to repeat this process.

f) Track record the prism amount 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 light. The wavelengths and colors of the spectral lines receive in the table below. While making measurements, unclamp and rotate the prism table to check that the prism is oriented for minimum perspective of deviation for the red, renewable, and blue lines.

When calculating very carefully spaced lines, like the two times yellow lines, make the slit very slim and check the concentration. When calculating dim lines, make the slit wider.

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