Name (printed) Destructive Interference. Constructive Interference
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1 Name (printed) LAB TWO DIMENSIONAL WAVE INTERFERENCE INTRODUCTION Tap a stick repeatedly in the water of a pond and you get what you ve always come to expect a succession of circular waves. It makes sense, because if the energy from the stick moves in all directions at the same rate, then the shape of the wave front would geometrically have to be a circle. But try tapping two sticks simultaneously and close together and you would see something very different. You would (if you looked closely enough) see an interference pattern (Figure 5.16). The pairs of outward moving circular waves from the two sources combine (or interfere) in a pattern that is absolutely motionless and stable. The pattern consists of lines (actually pairs of hyperbola) that represent regions of either constructive interference (crests from one source meeting crests from the other source) or destructive interference (crests from one source meeting troughs from the other source). The lines where constructive interference occurs are called antinodes or maxima. The lines where destructive interference occurs are called nodes or minima. To understand the physics of antinodes and nodes, first consider that the two sources of waves are separated by a bit. This means that when each of them is producing waves, there will be points out beyond the two sources where a wave from one source has traveled a different distance than a wave from the other. If the sources are in phase (in step with each other, producing pulses at the same time), then there will be points where the waves will no longer be in step. If at one point they are out of step by a full wavelength, then they are really, back in step. Crests are still aligned with crests and there would be constructive interference at that point Constructive Interference Destructive Interference Figure 5.16: Two sources of waves placed close together, and having the same frequency, will produce a stable interference pattern with regions of constructive and destructive interference. (Figure 5.17). This would also be true if the waves were out of step by two wavelengths (or any integer number of whole wavelengths). However, if the waves at one point were out of step by a half wavelength, then the crest of one would be in line with the trough of the other and they would cancel each other out. This would be a point of destructive interference (Figure 5.17). This would also be the case if the waves were out of step by one-and-a-half wavelengths (or any number of odd half wavelengths). Constructive Interference Destructive Interference Figure 5.17: If two sources of waves are separated by a bit when each of them is producing waves, there will be points out beyond the two sources where a wave from one source has traveled a different distance than a wave from the other. Depending on the difference in distance traveled, the waves can interfere constructively or destructively. 1
2 PURPOSE To recognize wave interference patterns. To learn to use wave interference patterns to calculate the wavelength of the waves causing the pattern. PROCEDURE (PART 1) 1. Set up the ripple tank as shown in Figure When the waves produced by the bobbers reach the end of the tank, they may reflect back, obscuring the interference pattern. If this happens, line the rim of the tank with paper towels to absorb the wave energy. 2. Set the wave sources at the proper distance apart and set the motor at the proper frequency so that a stable interference pattern is formed (Figures 5.16 and 5.19). QUESTIONS 1. State the relationship between the source separation and the space between the nodes. Specifically, what happens to the distance between the nodes when the distance between the sources (bobbers) increases? Figure 5.18: Ripple tank viewed from above. Note the paper towel wave absorbers. 2. State the relationship between the wavelength and the space between the nodes. (Increasing the motor frequency decreases the wavelength.) Specifically, what happens to the distance between the nodes when the wavelength increases? Figure 5.19: Bobbers producing an interference pattern. Note the flat nodes in between the rippled antinodes. 2
3 BACKGROUND FOR PART 2 m = 1 m = 0 m = 1 m = 2 m = 2 m = 3 x m = 3 m = 4 m = 4 L L θ Figure 5.20: Interference pattern measurements. S 1 d S 2 You ve seen that when two wave sources have the same frequency and are reasonably close together, they form a stable interference pattern. It s possible to calculate the wavelength of the waves producing this pattern with three measurements from the interference pattern. In order to make these measurements, a point must first be labeled on one of the antinodes. The location of this point is somewhat arbitrary, but should be in the center of the antinode and as far from the sources as possible. Any antinode can be chosen. After the point on the antinode is chosen, three measurements must be made (see figure 5.20): Then, to calculate the wavelength, λ, of the wave, use the following equation: d sinθ = mλ The diagram on the following page represents the image of an interference pattern. Choose a point on an antinode and make measurements to calculate the wavelength of the wave producing this interference pattern. Then measure in between two of the wave crests to check your calculation. L the distance from a point midway between the sources to the point on the antinode. x the distance perpendicular from the middle of the central antinode to the point on the antinode. d the distance between the centers of the sources. You also need to know the number of the antinode, m, that the point is on. Antinodes are numbered from the central antinode (m = 0), starting with m = 1. Antinodes are counted as positive when going either to the left or to the right of the central antinode. (The point in Figure 5.20 is on m = 2.) You can use x and L to calculate the angle, θ, shown in Figure Figure 5.21: Marking data on the projected image of a stable interference pattern. 3
4 Source 1 Source 2 Try to calculate the wavelength of the waves producing the interference pattern above by placing a point on an antinode (far from the sources) and then making measurements shown on the previous page. PROCEDURE (PART 2) Calculations 1. Establish an interference pattern with four clear antinodes on each side of the central antinode. Note the frequency of the motor and then don t change motor speed. If the motor speed changes, begin Part 2 again. 2. Locate four distant points on four different antinodes. It s very helpful to have two on each side of the pattern so the drawings don t get too crowded. Use pencils and a ruler to draw lines that show all variables d, x, L. 3. Measure and record d, x, L, and m for each of the points in the data table on the next page. 4. Call me over to make a measurement of your actual wavelength. 4
5 DATA AND ANALYSIS 1 Calculate the sinθ for each trial using x and L. 2. Calculate the wavelength for each trial as well as the average wavelength. 3. Calculate the experimental error: trial # m d (cm) x (cm) L (cm) sinθ λ (cm) Known wavelength: Average exp. wavelength: Percent error: Average wavelength CALCULATIONS TRIAL 1 TRIAL 3 TRIAL 2 TRIAL 4 GET CHECKED BEFORE MOVING ON 5
6 LAB LIGHT WAVE INTERFERENCE INTRODUCTION Isaac Newton was brilliant. It is said that he went from having a basic knowledge of college freshman math to being the most brilliant mathematician in the world in two years, and self-taught! In addition to his primary investigations of the physics of motion (three Laws of Motion and his development of the Universal Law of Gravity), he also investigated the physics of light. He believed there was adequate evidence to claim that the composition of light was that of particles (corpuscles, he called them) rather than waves and so it was accepted. Well, not by everybody. Over a century later, Thomas Young, a physicist and a physician had a brilliant idea to absolutely solve the problem of the true nature of light. He figured that if light were a wave, then two identical sources of light, placed closely enough together, would have to form an interference pattern. The nodes, in this case, would be dark regions where the light from one source cancelled the light from the other source. So he brought a thin sliver of light up to a card with two holes spaced very closely together and then let the resulting light fall on a distant screen. Oh, it must have been a glorious day, and I know that he must have wished that Newton were still alive to see the very simple experiment that disproved Newton s theory of light. Well, maybe Young didn t have that kind of rub your nose in it personality, but I m sure he was beside himself with excitement when he saw the alternating bright and dark spots on the screen onto which the light fell. And, I know that his immediate inclination was to calculate the wavelength of the light from the geometry of the interference pattern. You ll do the same in this recreation of one of the most important experiments in historical optics. However, before the actual measuring of the wavelength of light, you will do a qualitative investigation of the interference of light as it passes through multiple slits. At the conclusion of the qualitative portion, you should be able to predict Figure 5.22: Thomas Young s visualization of two sources of light waves interfering and causing characteristic antinodes (bright regions) and nodes (dark regions). how the interference patterns change when any of the following conditions changes: The distance between the openings changes. The number of openings changes. The wavelength of light used changes. PURPOSE To qualitatively investigate the physics of multiple slit interference of light waves. To use the physics of wave interference patterns to calculate the wavelength of light. 6
7 PART 1: A QUALITATIVE INVESTIGATION OF MULTIPLE SLIT INTERFERENCE Throughout this Part 1 of the lab, you will be making qualitative observations of interference patterns caused by light from either a red or green diode laser being directed through a variety of multiple slits in a PASCO Scientific High Precision Multiple Slits Wheel (see Figures 5.23 and 5.24). 1. Comparing differences in interference patterns when using double slit openings with different slit separations: In the Double Slits section of the wheel, direct the laser light through the most widely spaced double slits and the most narrowly spaced double slits. a. How is the interference pattern different in these two cases? b. Make a scale drawing below, labeling the two patterns produced with the different double slits. Figure 5.23: Light Wave Interference equipment. The diode laser is clamped behind the Multiple Slits Wheel. Light from the laser is directed through the desired pattern, producing an interference pattern on the screen in the background. 2. Comparing differences in interference patterns when using multiple slit openings with different numbers of slits: In the Multiple Slits section of the wheel, direct the laser light through the 2-slit opening and the 5-slit opening. a. How is the interference pattern different in these two cases? b. Make a scale drawing below, labeling the two patterns produced with the different multiple slits. Figure 5.24: High Precision Multiple Slits Wheel. There are a number of double and multiple slit patterns to direct laser light through. 3. Comparing differences in interference patterns when using different colors of light: In the Multiple Slits section of the wheel, direct green and then red laser light through the 5-slit opening. a. How is the interference pattern different in these two cases? b. Make a scale drawing below, labeling the two patterns produced with the different colors of light. GET CHECKED BEFORE MOVING ON 7
8 PART 2: A CALCULATION OF THE WAVELENGTH OF LIGHT 1. Direct either red or green laser light through the 5-slit opening in the Multiple Slits section of the wheel. You will see a series of bright antinodes (Figure 5.25). You can place the screen farther away in order to increase the size of the pattern. 2. Now make measurements similar to those made in the Two Dimensional Wave Interference Lab to calculate the wavelength of the light being used to create this interference pattern. In the last lab, you used the equation d sinθ = mλ to find the wavelength of the water waves. You know that this equation can also be expressed as λ = dx, where ml d = the distance between the slits (recorded on the wheel) x = the distance between the chosen antinodes (these should be the most widely spaced antinodes that you can reasonably measure with your calipers). m = the number of nodes between the chosen antinodes. L = the distance from the wheel to the screen. L Figure 5.25: Measure L from the wheel to the screen. Measure x between the most widely separated antinodes that can reasonably be measured with the calipers. m is the number of nodes between the chosen antinodes (four, in this photograph). 3. Repeat the instructions above for the other color of light. x DATA Color d (m) x (m) L (m) m Red Green 8
9 CALCULATIONS (SHOW ALL WORK) 1. a. Calculate the wavelength for red light. The conventional unit for wavelength is the nanometer (nm). 1 nm = 1 x 10-9 m. Express your calculated wavelength in nanometers. b. Calculate the percentage error from the actual wavelength specified by the laser. 2. a. Calculate the wavelength for green light in nanometers. b. Calculate the percentage error from the actual wavelength specified by the laser. 3. Obtain a slide with multiple slit patterns from me and determine the spacing between the slits in the center pattern. Show experimental setup, data table, and all calculations below. GET CHECKED BEFORE MOVING ON 9
10 QUESTIONS AND PROBLEMS WAVE INTERFERENCE 1. Specify the necessary condition for the path-length difference between two waves that interfere: a. constructively b. destructively? 2. Sources S1 and S2 are in phase. Point P is on the m = 6 antinode. Calculate the wavelength of the wave. S 1 S 2 P 3. What exactly causes the first node to the left (or right) of the central antinode to occur where it does? 4. What exactly causes the third antinode to the left (or right) of the central antinode to occur where it does? 5. Find the wavelength for an interference pattern from point sources 2.3 cm apart where a point on the first maximum is 2.4 cm from the central maximum, and 5.4 cm from the midpoint of the sources. 6. Two radio antennas simultaneously transmit signals of the same wavelength and in phase. A radio in a car receives the signals. If the car is at the second maximum of the interference pattern produced, what is the wavelength of the signals? Refer to the drawing on the right. 300 m 1400 m 27 m 10
11 7. A sound interference pattern is created using two audio speakers located 1.25 m away from each other. The first node is located at 10 from the central antinode. What is the pitch of the sound wave? GET CHECKED BEFORE MOVING ON 8. Two slits are cm apart. Monochromatic light is directed through the slits. The 3 rd order (m = 3) bright lines are 12.5 mm apart and are seen 0.40 m from the slits. What is the wavelength and color of the light? 9. Red light, having a wavelength of 650 nm is directed through two slits separated by mm. The distance from the slits to a wall where the interference pattern is formed is 2.35 m. What is the distance between the two 2 nd order bright lines? 10. Monochromatic light passing through two slits separated by cm falls on a screen 2.0 m away, producing the pattern to the right. What is the wavelength of the light? 11. If the light used in the problem above is directed through a different pair of slits, the pattern to the right forms on the same screen 2.0 m away. What is the distance between this pair of slits? 11
12 The last eight problems are for Honors Physics only 12. A soapy water film (n = 1.33) is in a plastic loop out in the sun. A portion of the film reflects all but the green light (λ = 550 nm). What is the minimum thickness of the film in that portion? 13. A plastic thin film (n = 1.37) with a thickness of 212 nm is placed on the lenses of a pair of sunglasses. If you looked at someone wearing these sunglasses in full sunlight, what color would the lenses be? 14. If you take the wand of a soap bubble maker and hold it so that the plane of the soapy water is vertical, there are colored bands containing each color of the spectrum from violet through red. Then they repeat themselves several times until the bottom of the soapy water in the wand. Explain the occurrence of the colored bands as well as why they repeat themselves. 15. If the wand in the previous question is held vertically for a long enough period of time, the color disappears from the bands at the top of the wand and then finally the film breaks. Explain the disappearance of the colors at the top of the wand. 12
13 16. A soap film is deposited on the surface of some glass (n = 1.50). A portion of it appears red (λ = 6.00 x 10-5 cm in a vacuum) when viewed from a right angle in white light. Determine the smallest non-zero thickness for that portion of the soap film if its index of refraction is How thick should the coating of a material be with an index of refraction of 1.35 on a piece of flat glass (n = 1.55) if you want it to be an anti-reflection coating for blue light (λ = 450 nm)? 18. A transparent film (n = 1.40) with a thickness of 1.10 x 10-7 m is deposited on a glass lens (n = 1.55) to form a non-reflecting coating. What is the wavelength of light (in vacuum) for which this film has been designed? 19. A certain transparent substance has an index of refraction of What is the thinnest film coating of this substance on glass (n = 1.50) for which destructive interference of green light (500 nm) can take place by reflection? The glass and film are in air. 13
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