Physics 1051 Laboratory #6 Diffraction. CD Diffraction

Transcription

1 CD Diffraction

2 Contents Part I: Setup Part II: The Diffraction Grating Part III: CD Groove Spacing

3 Part I: Introduction One of the goals in this lab is to use a diffraction grating to determine the wavelength of a laser pointer. The grating equation is m λ = d sin θ, m = 1, 2, 3, 4... where m is the order number, λ is the wavelength of light, d is the slit spacing of the grating, and θ is the diffracted angle. This expression illustrates that constructive interference occurs when the path difference δ is an integer number of wavelengths. Once the wavelength of the laser is known, it will be used to determine the groove spacing of a Compact Disc.

4 Apparatus You should have been provided with: Laser pointer Metre sticks CD Diffraction Grating of known slit spacing Mounting assembly Some sheets of white paper

5 Part II: The Diffraction Grating What happens when light passes through a diffraction grating? Put the diffraction grating in front of your eye and look around. What do you see? Look at the lights in the room through the grating. Can you explain their appearance using the grating equation? QUESTION 1: Explain the appearance of the room lights by considering the grating equation.

6 Setup: Determining the Wavelength Place your laser pointer in the groove in the base. Record the slit spacing written on your diffraction grating in your Activity Log. This is not simply the number of lines/mm! Position the diffraction grating in the slot in front of the laser. Place the screen in front of two posts which are screwed into the bench top. Use the clamps provided to fasten the screen so that it does not move. Tape some white paper to the front of your screen.

7 Setup: Determining the Wavelength Place the grating and laser assembly approximately 30 cm from the screen. Make sure the screen and diffraction grating are parallel by measuring the screen to grating distance on each side of the assembly. Measure the distance between the diffraction grating and the screen and record it along with the associated uncertainty in Table 1 of your Activity Log.

8 Making Your Mark! Shine the laser through the diffraction grating and make sure you observe a diffraction pattern. If you don t check that the laser is passing through the grating. Zeroth order The spot that appears in the middle is known as the zeroth order. Make a note on the screen as to which spot this is. Have your partner carefully mark the centre positions of at least 6 bright spots on each side of the zeroth order spot. 2nd QuickTime and a TIFF (Uncompressed) decompressor are needed to see this picture. 1st 1st 2nd zeroth order Note: You should be able to see at least 8 higher order spots on both sides of the central spot.

9 Calculations Remove the screen from the bench and lay it flat on the bench top. Measure the distance D between the two first order bright spots. Divide this distance by 2 to obtain the average distance, X, between either spot and the centre. Repeat this procedure to obtain the average distances for each of the six higher order spots. Record the distances in Table 3 of your Activity Log. θ L D Using your trigonometry skills, calculate the diffraction angles θ for all the spots you have measured. Using the grating equation, calculate the path difference δ for all the angles you just obtained, and record the values in Table 3 of your Activity Log.

10 Graphical Analysis Launch Graphical Analysis by clicking on the icon in the below. Use it to plot δ versus m. Calculate and display the regression line for this data set. To do so, pull down the Analyze menu and select Linear Fit. Then double click on the box that appears and in the Standard Deviations section check both the Slope and Intercept. Record the slope and intercept (and uncertainties) in Table 4 of your Activity Log. Print the graph and include it with your Activity Log. QUESTION 2: Using the diffraction equation and the slope of your graph, calculate the wavelength of your laser pointer. Be sure to include the uncertainty and units. QUESTION 3: Compare your calculated wavelength with the value quoted on your laser pointer. If they do not agree, explain why.

11 Part III: Get in the Groove! A CD consists of a series of evenly spaced (reflective) grooves and ridges that act as a diffraction grating. The grooves in a compact disc are very close together. One side of a disc can hold more music than two sides of a vinyl record. Just how close are the grooves? To measure the distance between the grooves we will inspect the diffraction pattern from your laser of known wavelength using the diffraction equation. CDs are reflective and therefore the diffraction pattern can be observed by looking at the reflected pattern. When you look at the side with the grooves in it you see a rainbow spectrum. The rainbow spectrum is from the reflection of white light that has been diffracted.

12 Setup: Groovy Spacing Remove the diffraction grating from the holder and replace the paper on your screen with a new piece. Be sure to punch a hole in the paper where the hole is in the screen. Place the screen in the slot in front of the laser pointer and carefully align it such that the laser clearly passes through the hole in the screen and paper. Fasten a CD in the clamp provided and attach it to one of the support bars. Slide the laser and screen assembly onto the other support bar and tighten the anchor screw. See photos of the setup on the next page

13 CD Setup Photos

14 Setup: Groovy Spacing Shine the laser so that it reflects from the outer region of the compact disc, where the tracks of the CD are approximately parallel lines. To ensure that there is normal incidence of the laser on the CD, carefully move the CD until the central spot is reflect back onto the incident beam. This step is tricky but very important. Take your time! You will have to rotate, raise/lower and tip the CD until the pattern is lined up properly. The interference pattern on the screen should be horizontal.

15 On Your Mark! In order to observe the second order diffraction pattern from the CD, the distance between the screen and the CD should be no more than 25 cm. The groove spacing will be calculated using both the first and second order diffraction maxima. If you do not see the second order maximums consult your instructor. It is very important to ensure that the diffraction pattern you measure lies along the horizontal line containing the hole punched in the screen. This shows that the apparatus is correctly aligned.

16 On Your Mark! Measure the distance between the screen and the CD and record it along with the associated uncertainty in Table 5 of your Activity Log. 1st As before carefully mark the centre positions of the first and second order bright spots on the screen. The zeroth order spot is located at the hole in the screen. zeroth order Remove the screen from the slot and measure the distance, D, between each of the higher order diffraction spots. Half this distance to obtain the average distance, X, from that spot to the zeroth order and record them in Table 6 of your Activity Log. Shown at right is the distance between the two first order bright spots. 2nd D Quick Time and a TIFF (Uncompressed) decompressor are needed to see this pictur e. 1st 1st 2nd zeroth order (located at the hole)

17 Calculations Using your trigonometry skills, calculate the diffraction angles for all the spots you have measured. Calculate the groove spacing, d, using the diffraction equation and the information you have just obtained for m=1 and m=2. θ x L QUESTION 4: Calculate the average groove spacing of your CD. Be sure to include the uncertainty and units.

18 What did you learn? Answer the following questions in your Activity Log. QUESTION 5: What would happen to the interference pattern if you increase the track width of the grooves on a CD? Why? QUESTION 6: Why can a CD be used as a diffraction grating? That is, how is a CD similar to a diffraction grating? QUESTION 7: What is the smallest value of d for which an interference pattern is produced? Could this interference pattern be observed in our experimental setup? Explain.

19 Wrap it up! Check that you have completed all the Tables of your Activity Log. Make sure that you have answered all the Questions completely, Attached to your Activity Log should be your graph of path difference δ versus order number m.