EXPERIMENT 12 THE WAVELENGTH OF LIGHT; THE DIFFRACTION GRATING

Transcription

1 EXPERIMENT 12 THE WAVELENGTH OF LIGHT; THE DIFFRACTION GRATING INTRODUCTION: One of the most fascinating chapters in the history of physics has been the search for an understanding of the true nature of light. The search to discover whether light is a particle or a wave, which extended over three centuries, has been in large part abandoned-- not because the answer is known, but rather because most physicist now agree that the question is meaningless. In this experiment you will observe the formation of spectra by a diffraction grating-- an experiment which was once considered positive evidence that light is a wave. THEORY: A grating consists essentially of a large number of fine, evenly spaced, parallel slits. There are two types, transmission gratings and reflection gratings. In the former type, used in this experiment, lines are ruled on glass, the unruled portions acting as slits; in the latter type, lines are ruled on a polished metal surface and the incident light is reflected from unruled portions, effecting by reflection the same results as is secured by transmission in the other type. Gratings are usually ruled with from 10,000 to 20,000 lines to an inch. Consider a parallel beam of monochromatic light falling on the grating from the left. Huygen s principle asserts that each of the grating slits can be considered a new source of light as shown by the wavelets to the right of the grating in Figure 1. A new wave front is constructed by drawing the envelope that connects these wavelets. This new wavefront propagates directly ahead ( as shown by the dotted waves and rays) and is brought to a focus by the telescope at C. This is called the central image of the grating.

2 However, other wavefronts can also be constructed from the original Huygen s wavelets. One such set is shown by the solid waves and rays in the region to the right of the grating. This set of waves will be focused by the telescope to a point displaced from C, the angular position being given by, sinθ = λ d (1) where d is the distance between adjustment slits in the grating (called the grating constant), and λ is the wavelength of light used. Since λ varies of different colors of light, a spectrum is formed in this region. Other wavefronts can be constructed by choosing every second (or third) wavelet from adjacent slits, so that the general form of equation (1) is (2) n λ = d sinθ where n is called the order number. The angle between the ray emerging from the grating and the ray incident up on the grating is called the angle of deviation. The value of this angle depends, among other things, upon the angle of incidence. If the angle of incidence is zero degrees, that is, if the grating is normal to the ray of light, equation (2) applies. There is a certain angle of incidence, however, for which the deviation produced has a minimum value. When this condition exits, the grating is said to be in a position of minimum deviation. Measurements of wavelength are somewhat simplified by using the grating in this position. When so used, the wavelength is given by the relation (3) n λ = 2 d sin(d/2) where all quantities have the same meaning as before and D is the minimum value of the deviation. THE EXPERIMENT: 1. APPARATUS: The experimental apparatus consists of: a discharge tube with its high voltage power supply, a spectrometer, and a diffraction grating (600 lines/mm). All of these parts are provided in your laboratory station. 2. PROCEDURE: CAUTION: Be sure not to touch the grating surface. Study the spectrometer and follow the instruction described in the previous experiment for the measurement of the index of refraction. Locate the collimator, the telescope, the grating table, and the slit, as well as the set and slow motion screws for

3 each. Place the telescope and the collimator approximately in line. Be sure you know how to read the scales. The main scale is graduated in degrees and half degrees, and the vernier reads to minutes. Now that you are familiar with the spectrometer, you should follow the following experimental procedures: 1. Switch on the discharge tube. 2. After the arc has been lighted, see that the slit is opened but never more than one millimeter. Focus the telescope so that you have a distinct and well-illuminated image of the slit. 3. Turn the grating table so that the incident light is approximately normal to the grating. You will see an image of the slit and use this same edge throughout the experiment. Obtain and record the scale reading. 4. Rotate the telescope left (approximately 18 ) until the intense green line is approximately in the center of the field of view. 5. Rotate the grating table in the same direction. You will notice that the green line rotates in the opposite direction for a short distance and then, after further rotation of the grating, the line moves in the same direction. Set the grating table at the point of reversal. Set the cross-hair on the line by means of slow motion screw. Check the setting of the cross-hair by small rotations of the grating in both directions. You now have the grating set at the angle of minimum deviation. For accurate work, the slit should be moderately narrow. 6. Read the vernier and record the angle. 7. Rotate the telescope in the same direction as before until this green line appears a second time. This is the second order and is about 36 from the central image. This line is very faint and, therefore, you may have to widen the slit if possible and set the cross-hair on the line. Record your data on the worksheet. 8. Repeat steps (4) through (7), this time going to the right. Record your data on the worksheet. ANALYSIS OF RESULTS Calculate the angle of minimum deviation for each of the four observations. Use the Equation (3) to calculate the wavelength of the light. Give the final answer in Angstroms. Five-place accuracy is suggested. Show your work in the space on the worksheet with explanatory remarks as required. QUESTIONS: 1. The central image at C is sometimes called a white image. Why? 2. What is the maximum order number you might expect to see with the grating you have at your station with λ = 4500Å and 8000Å? Explain. 3. What advantages might you expect to result from using a grating to form a spectrum opposed to using a prism?

4 4. Using Equation (2) can you judge whether the first order or the second order measurements seem more accurate than the other?

5 AUI PHY 1402 LAB. REPORT EXPERIMENT 12 THE WAVELENGTH OF LIGHT; THE DIFFRACTION GRATING NAME:.. DATE:.. SECTION:.. * * * 1. EXPERIMENTAL PURPOSE: State the purpose of the experiment.( 5 points ) 2. EXPERIMENTAL PROCEDURES AND APPARATUS: ) Briefly outline the apparatus used and the general procedures adopted. (5 points

6 3. RESULTS AND ANALYSIS Grating Spacing (lines/mm). Grating Constant (mm/line). (10 points) (35 points) TABLE 1: n central vernier reading minimum deviation (D) λ left right Calculations of Minimum Deviation and λ ( show your work) (25 points)

7 4. CONCLUSION: (5 points) QUESTIONS (15 points)