214 LABORATORY EXPERIMENT: Dispersion of Light by a Prism   Objective: To determine how the index of refraction of glass varies with wavelength. Apparatus: Spencer spectrometer, helium spectral tube, spectrum tube power supply, equilateral glass prism (3 by 60 degrees), low power lamp, platform (10 to 12 inches high) for tube power supply, prism clamp. Theory: The index of refraction of a material is defined as

                            (1)

where c = velocity of light in vacuum and  v = velocity of light in the material. It is found that for most types of glass the velocity of light in glass varies with the wavelength that the light had in vacuum. Therefore n also varies with wavelength.As light goes from air into glass, the angle of refraction can be found from

   (2) Since nglass varies with wavelength, so does the angle of refraction. Thus when a beam of light is refracted, the different wavelengths will be bent by different amounts. This phenomenon is called dispersion. Dispersion explains the separation of white light into a spectrum by a prism or in a rainbow.

      Figure 1 shows light passing through a prism. The light is bent once on entering the prism and again when exiting. The angle between the original and final directions of the light is called the angle of deviation. The angle of deviation could always be found by applying the law of refraction at each surface.

      The angle of deviation changes as one changes the angle of incidence at the first surface. However it can be shown mathematically that the minimum angle of deviation occurs when the light ray passes symmetrically through the prism as in Figure 2. Then it can be shown that when A = apex angle of the prism and D = minimum angle of deviation, the index of refraction is

                                   (3)

General Considerations about the Experimental Method: Since the index of refraction of glass only varies slightly with wavelength over the visible spectrum:

1. A precision spectrometer is used with which angles can be measured to the nearest minute. Since 1 degree = 60 minutes, an angle of 50 degrees (typical in the experiment) contains 50 X 60 = 3000 degrees, so 1 minute

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accuracy is 1 part in 3000 or .033%.

2. For the light source a helium gas discharge tube is used. The visible spectrum of helium consists of twelve discrete wavelengths, each known very precisely ( <.001 % ). For each wavelength a measurement and a calculation will yield the value of n for thatwavelength.

3. The sample of glass being studied is made into a prism wit three angles of exactly 60 degrees ( to better than 1 minute.)

4. The minimum angle of deviation is measured separately for each helium wavelength. From this the index of refraction can be calculated from equation 3. The advantage of this method is that only one angle needs to be measured to determine the index of refraction.

Description of the Spencer Spectrometer: Its essential parts - see Figure 3 - are a telescope T, a collimator C rigidly attached to the base, a table B and a platform P which carries two fiducial marks and associated verniers V, 180 degrees apart. The telescope and the table can be independently rotated around a common vertical axis, their relative orientation being indicated by the reading of the fiducial marks on the divided circular scale which rotates integrally with the telescope. The table B which may also be independently rotated, may be locked to the platform by means of the clamping screw G. The telescope position can be locked with clamping screw L and then its position finely adjusted by turning screw M. The table position can be locked with clamping screw K and then its position finely adjusted by turning screw N. The collimator is provided with a slit aperture whose width can be adjusted by turning the knurled ring S.

      Please make only the adjustments listed below and in the Procedure. DO NOT FORCE ANY PART TO MOVE OR CLAMP ANY PART TOO TIGHTLY.

1. The eyepiece: hold your eye close to the telescope ( with your glasses on) and look through the telescope, with your eyes perfectly relaxed, at a featureless sheet of paper and slide the eyepiece gently in and out until the crosshairs are sharply defined. Notice that the crosshairs are fixed in the barrel of the telescope and cannot be readily rotated.

2. The telescope: sight upon a distant object ( so that parallel rays enter the telescope ) and by turning the knurled ring F bring the "object" into focus with the crosshairs. Move your eyes sideways and make fine adjustment to the focus ( with ring F ) until there is no relative motion between the object and the crosshairs. (Then the images of the object and the crosshairs are in the same plane and there is no parallax between them. )

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Read the following while looking at the apparatus scales:

Figure 4 shows a typical reading of the angular position of the telescope 1. The base scale (outside scale ) goes from 0 to 360 degrees and is marked at each half degree. 2. Note that the zero line of the vernier lies between 47.5 and 48 degrees. Thus the angle being read is 47.5 degrees plus some fraction of a half degree. A half degree is 30 minutes. 3. The vernier scale divides the half degree into 30 minutes. On Figure 4 note that the 22 minute mark lines up best with the base scale. 4. So the reading is

      47.5 degrees + 22 minutes   =  47 degrees and 30 minutes + 22 minutes   =  47 degrees and 52 minutes

Procedure: 1.Place the spectrometer box near the end of the lab table. Put the spectrometer on top of it with the collimator pointing toward the center of the table.

2. Adjust the telescope crosshairs and focus as instructed in the spectrometer description.

3. Carefully place the helium spectrum tube into the spectrum power supply, and stand the spectrum power supply on the 10 to 12 inch high platform. NOTE - THE SPECTRUM POWER SUPPLY IS RATED AT 5000 VOLTS. DO NOT TOUCH THE CONTACTS. Align the collimator so that the light will go straight through it. Turn the power supply on.

4. Initially adjust the collimator slit to be wide. Align the telescope and collimator. Look through the telescope at the image of the slit and adjust the slit to be narrow. You should see a very clear, narrow image of the slit. If you don't, ask for help from the instructor.

5. Lock the spectrometer table in place. (The platform is the six inch diameter black disk. )  The table should remain in this position throughout the experiment.

6. Align the telescope on the narrow image of the slit. Choose one of the two verniers and read the angular position. (Refer to the sample reading described in the spectrometer description to make sure you are reading the angle correctly. ) Then ask the instructor to verify your reading. Later this angle will be referred to as o.

7. Place the prism on the spectrometer table. (That is the three inch diameter silvery disk.) Clamp the prism in place as shown in the figure.

8. Rotate the telescope as in the figure until you see the spectrum of helium light that has passed through the prism.

9. Examine the colors of the helium spectrum and carefully match them with the wavelengths of helium in the reference. Note that some of the wavelengths may be too dim to see. Use only the ones that you can identify with certainty.

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10. To measure the minimum angle of deviation for a certain spectral line, follow steps a to c below. Use the bright red line first (667.81 nm).

a. View the bright red line with the telescope. Slowly rotate the spectrometer platform containing the prism, meanwhile watching the bright red line. You should be able to see the red line move sideways, then stop, and move back the other way. The prism position where the red line stopped is the orientation for minimum deviation for that line.

b. Place the telescope crosshairs on the image of the red line and read the angular position, using the same vernier as before. This angle will be referred to as .

c. Repeat a and b, taking care to find the exact point that the red line stops moving.

d. Later you will calculate  D = o = angle of minimum deviation for that wavelength.

11. Choose another clearly identified spectral line and repeat all of step 10 for that line (instead of red ). Then repeat step 10 again for each other identified spectral line. Analysis: 1. For and each show your original readings in degrees and minutes. Then convert each to degrees and decimal fractions of a degree as in this example.

      53 degrees and 37 minutes   =  53 and 37 / 60 of a degree   =  53.6167 degrees

Show also the converted values of and each .

2. For each spectral line calculate the minimum angle of deviation from       D = D = o               (4 )

3. For each spectral line calculate the index of refraction at that wavelength using equation number 3.

4. Plot index of refraction versus wavelength in nm.

5. The Cauchy equation expresses n as a function of wavelength by

                       ( 5 )

Convert each wavelength to meters. Then calculate for each, plot n versus  and find a best

linear fit (trendline). From the equation of the trendline list your values of the constants A and B.

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Figure 6

Key Number Wavelength (nm) Color121110

706.52667.81587.56

Red (pale)Red (bright)Yellow

If a pale line appears between lines 10 and 9 (where the dotted line is) ignore it. It is not a true spectral line.987654321

504.77501.57492.19471.31447.15438.79414.38412.08402.62

Green (pale)Green (bright)Blue – greenBlueViolet (bright)VioletVioletVioletViolet

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