Physics 1051 Laboratory #6 Diffraction CD Diffraction Physics 1051 Laboratory #6 Diffraction Contents Part I: Introduction Part II: The Diffraction Grating Part III: CD Groove Spacing Physics 1051 Laboratory #6 Diffraction Part I: Introduction n this lab a diffraction grating is used to determine the wavelength of a laser pointer which is, in turn, used to determine the groove spacing of a CD. 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. Physics 1051 Laboratory #6 Diffraction 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 Caution: You will use a laser in this experiment. If not used carefully, it may result in permanent eye damage. Do not shine it in anyone’s face. Do not point it around the room. Anyone with unsafe behaviour will be asked to leave and receive a a grade of 0 in the lab. Physics 1051 Laboratory #6 Diffraction Part II: The 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. QUESTION 1: Describe the appearance of the room lights when looking through the diffraction grating. Explain the appearance of the room lights. Physics 1051 Laboratory #6 Diffraction Setup: Determining the Wavelength Place your laser pointer in the groove in the base. Determine the slit spacing, d, using the number written on your diffraction grating. Record this in Table 1 of your Activity Log. d 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. Physics 1051 Laboratory #6 Diffraction 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 2 of your Activity Log. Physics 1051 Laboratory #6 Diffraction Making Your Mark! Shine the laser through the diffraction grating and make sure you observe a Zeroth order diffraction pattern. If you don’t, check that the laser is passing through the grating. 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 Q u i c k T i m e ™ a n d a T I F F ( U n c o m p r e s s e d ) d e c o m p r e s s o r a r e n e e d e d t o s e e t h i s p i c t u r e . centre positions of at least 6 bright spots on each side of the zeroth order spot. 2nd 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. Physics 1051 Laboratory #6 Diffraction Calculations Remove the screen from the bench and lay it flat on the bench top. θ Y L Measure the distance Y 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. Physics 1051 Laboratory #6 Diffraction Calculations continued Using your trigonometry skills, calculate the diffraction angles θ for all the spots you have measured and record them in Table 3. Using the grating equation (refer to introduction), calculate the path difference δ for all the angles you just obtained, and record the values in Table 3 of your Activity Log. Be sure you are using the right numbers in the diffraction equation. You may need to refer to the introduction to recall what each symbol represents. Physics 1051 Laboratory #6 Diffraction Graphical Analysis Launch Graphical Analysis by clicking on the icon in the below and 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 the results in Table 4 of your Activity Log. Before proceeding, have an instructor come check your graph, fit, and slope and initial your lab report. Print the graph and include it with your Activity Log. QUESTION 2: Using the diffraction equation and the slope of your graph, determine 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. Physics 1051 Laboratory #6 Diffraction 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 When you look at the side with we will inspect the diffraction pattern from your the grooves in it you see a rainbow spectrum. The rainbow laser of known wavelength using the diffraction spectrum is from the reflection equation. of white light that has been diffracted. CDs are reflective and therefore the diffraction pattern can be observed by looking at the reflected pattern. Physics 1051 Laboratory #6 Diffraction 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 Physics 1051 Laboratory #6 Diffraction CD Setup Photos Physics 1051 Laboratory #6 Diffraction 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 i.e. central spot reflects back through the hole. 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. Physics 1051 Laboratory #6 Diffraction 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. Measure the distance between the screen and the CD and record it along with the associated uncertainty in Table 5 of your Activity Log. Physics 1051 Laboratory #6 Diffraction On Your Mark! As before carefully mark the centre positions of the first and 1st 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, Y, between each of the higher order diffraction spots. Record these values in Table 6 of your Activity Log. Y Halve this distance to obtain the average Q u i c k T i m e ™ a n d a T I F F ( U n c o m p r e s s e d ) d e c o m p r e s s o r a r e n e e d e d t o s e e t h i s p i c t u r e . distance, X, from that spot to the zeroth order and record them in Table 6 of your Activity Log. 2nd 1st 1st 2nd Shown at right is the distance between the two first order bright spots. zeroth order (located at the hole) Physics 1051 Laboratory #6 Diffraction Calculations Using your trigonometry skills, calculate the diffraction θ angles for all the spots you have measured. L x Calculate the groove spacing, d, using the diffraction equation and the information you have just obtained for m=1 and m=2. QUESTION 4: Calculate the average groove spacing of your CD. Be sure to include the uncertainty and units. You may approximate the uncertainty using δdave/dave = δλ/λ+ δX1/X1+ δL/L Physics 1051 Laboratory #6 Diffraction What did you learn? 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 s 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. Physics 1051 Laboratory #6 Diffraction 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.