Laboratory Exercise. Wave Properties

Transcription

1 Laboratory Exercise Wave Properties INTRODUCTION A wave is an oscillation of some kind which transfers energy. The wave can be the physical displacement of matter (a mechanical wave) as happens with an ocean wave. A wave may also be an oscillation of some physical property such as the oscillation of electromagnetic charges that produce what we call light. In a mechanical wave a force displaces the matter (medium) through which the wave travels and then is returned to its original state by some restoring force. In the ocean wave example the deforming force may be the wind or a pebble dropped onto the surface; the restoring force is gravity. Sound waves work in a similar manner. Waves, such as electromagnetic waves, that transfer energy without a medium are oscillations in some fundamental property of matter, such as electric charge, in the case of electromagnetic waves. Since the charge is what oscillates, rather than matter, an electromagnetic wave can travel through space. You may have heard the term field in relation to waves but I deliberately avoided using this term since it is usually misunderstood. We will address the concept of field in the section on quantum mechanics (field theory). Exercise 1 Wave Properties The anatomy of a wave and the terms used to describe a wave form are shown below: There are three basic characteristics used to describe waves. 1. Frequency The number of waves produced in a given time period. This is usually measured in waves per second called Hertz (Hz). 2. Wavelength The length of a wave. This can be measured easily from crest to crest or from trough to trough. 3. Amplitude The height or depth of a wave. The amount of energy carried by a wave is related to amplitude. A high energy wave is characterized by high amplitude; a low energy wave by low amplitude.

2 Objective Materials The purpose of the lab is to study the types of waves and their properties using a slinky. Slinky, meter stick, camera, pencil Procedure AFTER COMPLETING THIS EXERCISE PUT DRAWINGS, PICTURES, VIDEOS, MEASUREMENTS, AND OBSERVATIONS ON YOUR WEB SITE. 1. On a smooth floor, stretch the slinky out between you and a partner. (Caution Do not over stretch the slinky!) Take video of the following activities in order to analyze using LoggerPro. Include LoggerPro analysis on your web site 2. Send a single wave to your partner. 3. Observe what happens to the wave when it reaches your partner s end. Observe the reflected wave. 4. Move one end of the slinky back and forth on the floor repeatedly (see diagram below). Create a series of standing waves. 5. Use LoggerPro to analyze both the anatomy and characteristics of the wave forms you created. 6. Now both you and your partner should produce a wave from your ends of the spring. You should both move the slinky to your own right (since you are facing one another this will be in opposite directions). Film the wave form as it propagates and then analyze its shape as the waves superimpose on one another. Sketch the wave in three locations; a. As the waves approach b. As the superimpose c. As they travel away from each other The superposition of waves is the key concept in the next exercises on constructive and destructive interference of waves. 7. Next create a series of waves by moving your hand towards and away from your partner (see the diagram below). Observe this wave and how it travels. This is the type of mechanical wave that transmits sound

3 Exercise 2 Mechanical Wave Interference In the not too distant past the properties of waves were most often studied using a wave tank. Wave tanks are shallow basins with a glass bottom. The basin is filled with water and a light suspended above the tank. As ripples are made in the tank the water acts as a lens and projects a series of shadows beneath the basin. They were difficult to set up, hard to calibrate, and wet. With the advent of computer simulations the process of wave tank analysis has become much drier. Objectives Materials Visualize interference patterns waves from two sources superimpose. Visualize interference patterns created using a two slit grating Use Young s equation to determine the wavelength of a laser light source. Computer Making predictions - your hypothesis Figure 1 Wikimedia Commons 1. Draw the pattern made by water waves that would propagate from two sources point of the same frequency in a wave tank. The waves would be produced in phase (same time and distance from the end of the tank. What would you expect to see on the screen below a wave tank where the waveforms intersect? 2. Download the zip file ripple from the class web site or locate and download the file by search on Falstad ripple tank simulation. (There are undoubtably others but this is one of the best that I have found.) 3. You can watch, and be mezmerized, by a single source waveform for a second or two but now set the simulation to two sources(top right of simulation window). Move the sources with your mouse so they are both a short distance apart on the left side of the simulated tank (same configuaration as your prediction above). It will be easier to watch if you slow both the frequency and the simulation speed down using the slider controls to the right of the tank. What pattern emerges as the two wave forms meet and superimpose? You may either take a screen shot for your web site or embed the simulation directly into your website to make an interactive for your site visitors. Go ahead and play with the controlsof the simulation. I have found this is an excellent way to visualize wave forms. The only drawback is that the forms are not quantifyable so you can do little more than visulaize what happens.

4 4. Set the simulator to produce a single point source and then change the mouse to Mouse=Edit Walls. You can now draw barriers inside the tank. Draw a barrier completely across the tank that has two small, closely spaced slits in it. (see at right). Don t worry that the walls aren t nice and straight. Now, observe the resultant wave form on the side of the barrier away from the source. How would you describe the waveform coming from each of the slits? You are welcome to play with the simulation. Check out some of the other Setups. We will be using lenses in later labs and the simulations may help you to visualize what is happening in those labs. Procedure AFTER COMPLETING THE LAB INCLUDE ALL PHOTOGRAPHS, SCREEN SHOTS, AND ANALYSIS INTO YOUR WEB SITE. INCLUDE DATA TABLES. INCLUDE EXPLANATIONS AND ANSWERS TO QUESTIONS IN YOUR SITE AS WELL. Part 1 Double Slit Diffraction In this exercise you will observe the patterns created when a coherent, in phase, light source (laser) passes through double and then single slit gratings. After observing the effect with a real laser you will use another computer simulation in order to quantify the phenomenon. At some time in the future we may be able to take live measurements but at this point the computer simulation works better than our equipment allows. 1. Mount the red laser pointer on the optics bench along with the plastic double slit diffraction grating. Position the pointer and the grating so that it will hit the center of the two slits. The grating should be about 10 cm from the grating. With the lights off shine the laser through the grating so that it casts a pattern on a screen positioned at least a meter away. (A piece of tag board attached to the wall works well. Observe the interference pattern created by the laser and photograph the result. Without changing any distances replace the double slit grating with the single slit grating. Note any differences in the interference pattern and photograph as before. 2. Browse to the website address < and download the simulation. The file is also posted on the class physics web site. Be patient, it may take a while for the simulation to load. 3. Using the default red light set up a double slit barrier with these initial settings; (amplitude=default, two slits, slit width=~500nm, slit separation= ~1230 nm, barrier=~1300nm, show screen on, intensity graph on). The settings are approximate due to the resolution of the sliders; you will use the measuring tape tool to get accurate measurements. Look at the resultant image on the screen and the intensity graph. Explain the central bright spot directly across from the middle slit barrier. 4. One the clearest explanations of the two slit wave phenomena that I have found is at Watch both lessons 2 and 3 before continuing.

5 5. Use the measuring tape tool to get accurate measurements for; Slit Width (w) = Slit Separation (d) = Barrier Distance (D) = Distance to 1 st maxima (y) = Slit width and slit separation should be close to the values you set with the slider, barrier distance is the distance from the front of the barrier to the screen. The setting you made with the slider was the distance from the light so that value will be different. Use the measuring tape to measure the path that a single light ray must follow from the front center of each slit to the center of the first maxima (m = 1) above the center bright maxima (m = 0). Be sure to measure to the screen plane and not the intensity graph. Top Slit Path Distance (r1) = Bottom Slit Distance = (r2) Δ r = What does the Δ r value tell you? The diagram below shows the geometry of the wave paths It is very difficult to actually measure the path difference accurately since the values are so small (not many measuring tapes have nanometer resolution) so the value you determined for Δ r which is the wavelength (ʎ) of the light source must be determined from known quantities. With a little geometry magic the relationship d sin Θ = m ʎ -or- ʎ = d sin Θ when m is 1 maxima can be derived. The magic part is that the two light rays, r1 and r2, must be considered parallel. This is not too much of a stretch since the distance D is so great compared to the differences in r that screen may be considered to be at infinity which is where parallel lines meet. A value for Θ can be derived using tan Θ = y/d. Note that one value you measured is not used in the determination of the wavelength. Once you finish your calculations try changing the slit width to see what effect it has. Remove the screen and the barrier. Turn the amplitude up so you get bright wave lines and then run the simulation for a short time. Pause the simulation and use the measuring tape tool to directly measure the wavelength of the light source. Compare the two values for ʎ that you calculated from the simulation with the value you measured directly. Report the % error on your web site.

6 Part 2 Single Slit Diffraction Now we will look at why an interference pattern occurs when in phase light is passed through a single slit. Hopefully you noticed in the question #4 in the predictions that when light passed through two slits it appeared to look like two separate light sources, very similar as to when you had two light sources without any barrier. So why does a single slit produce an interference pattern? It ends up that every point on the wave front can be considered as propagating. This provides not just two light sources but an infinite number of sources that all interfere with each other to produce the next wave form. Since light is an oscillation of electrical charges this makes some sense even though it is difficult to conceptualize. You have already photographed single slit interference so difficult or no it does occur. For a good, although fairly long explanation try: 1. Go back to the first simulator and use the single slit setup. Push the simulation speed all the way down and the resolution all the way up. Compare the magnitude (brightness) of the center maxima, m0, with the maxima to either side. How does this differ from the two slit pattern? Take a screen shot for your web site. 2. Now open the second simulator again and set the amplitude to the maximum brightness, Slit Width to ~500, Barrier Location to ~2100. You should see a strong central band and then the first minima on the screen chart. Notice from the diagram below how the successive maxima decrease in intensity (you will not see this in the simulation). Using the same geometric reasoning as used to determine the parameters of the double slit barrier you will come up with the equation; a sin Θ = m ʎ There are two difference between this equation and the one we developed for the two slit barrier; 1) a is the size of the slit, and 2) the m is for the minima rather than the maxima of the wave form projection. What this means is that you will be finding ½ ʎ rather than a complete wavelength at the position of the first minima. 3. Use the measuring tape tool to get accurate measurements for; Slit Width (a) = Barrier Distance (D) = Distance to 1 st minima (y) = 4. Calculate the wavelength of the light source from your measurements. Compare the value for ʎ that you calculated from the simulation with the value you measured directly. Report the % error on your web site

7 Part 3 Multiple Slits Using a Diffraction Grating In the lab exercise you will be doing a modified version of Young s experiment. He was incapable of doing this exercise with the technology available to him at the time. Rather than two closely spaced slits you will use a film with 500 (A) and 1000 (B) lines per millimeter. You will also use a single wavelength light source (laser). The physics is very nearly the same and you will be using much the same method of mathematical analysis that Young used. Objectives Use the mathematics of wave superposition to determine the wavelength of laser light sources. Materials Optics Bench and Hardware 1000 lines/mm diffraction grating 500 lines/mm diffraction grating Laser Pens (red, green, violet) Metric rule Colored Pencils DO NOT SHINE THE LASERS INTO ANYONE S EYES. CAREFULLY AVIOD REFLECTED LASER LIGHT. ALTHOUGH IT MAY NOT BE IMMEDIATELY EVIDENT LASER LIGHT WILL CAUSE DAMAGE TO EYES. Making predictions - your hypothesis 1. Hold one of the diffraction gratings up to the light. As you move the grating you will see a series of rainbows either above or below the light depending on the orientation of the grating. During the lab you will orient the grating so that the images produced are in the horizontal plane. Note the sequence of colors on each side of the light source. Also note if they are in the same order on the opposite sides of the light source. 2. In this exercise you will be shining different color lasers through the two gratings. The laser light will be diffracted in the same way as the white light you looked at in (1). Using colored pencils predict what the diffracted image of the lasers will look like. You can go back to the PhET simulation and change colors to help you in predicting.

8 Procedure Set the optics bench up so that the different lasers can pass light through the diffraction gratings. Try different distances from the laser to the grating while shining the laser at the wall. 1) Does it make a difference how close the laser is to the grating? 2) Does it make a difference how close the grating is to the wall? 1. Securely fasten one of the lasers so that it shines through the 500 l/mm grating. 2. Be sure that the optics bench is normal (perpendicular) to the wall. 3. Carefully measure and record D in mm (the normal distance from the grating to the wall). Use the same distance (D) throughout the exercise. 4. Carefully measure and record the distances y1 and y2 in mm. (Note: You may have difficulty seeing the second maxima no worries one will work) 5. Repeat the process for each laser. 6. Replace the 500 l/mm grating with the 1000 l/mm grating and perform the same measurements. Data LaserColor D (mm) Grating size Y1 (mm) Y2 (mm) 500 l/mm 500 l/mm 500 l/mm 1000 l/mm 1000 l/mm 1000 l/mm Analysis 1. Using your data determine Ɵ for each of the three lasers and the different gratings. Show your calculations and record answers in the analysis table. Again, you may not be able to determine the location of the 2 nd maxima. m2 m1 Ɵm2 Ɵm1 m0

9 Laser Ɵ 500 l/mm Ɵ 1000 l/mm 2. Knowing that Maxima (bright spots) are formed when wave forms interfere constructively at whole wavelengths provides us with a way to calculate the wavelength of each laser. Using the diffraction grating formula; ʎ = d sin(ɵm) m determine the wavelength of each laser. (d = space between two adjacent lines on the diffraction grating, m = interference maxima) 3. Record your calculated wavelengths in the analysis table and show your calculations. Laser ʎ w/500 l/mm grating ʎ w/1000 l/mm grating Average of two gratings Accepted ʎ % Error