Name Date Lab Time Lab TA PHYSICS 116 INTERFERENCE AND DIFFRACTION IMPORTANT SAFETY NOTE: PARTS OF THIS LAB INVOLVE THE USE OF HELIUM-NEON LASERS. THESE LASERS WILL NOT BURN YOUR SKIN BUT CAN CAUSE EYE DAMAGE. IT IS SAFE TO VIEW THE REFLECTION OF THE BEAM OFF OF A PIECE OF PAPER. NEVER LOOK DIRECTLY INTO THE BEAM OR ALLOW A REFLECTION OFF OF A MIRROR-LIKE SURFACE TO ENTER YOUR EYE. NEVER POINT THE BEAM OR ITS REFLECTIONS AT ANYONE ELSE'S EYES. APPARATUS Cardboard, pins, two wave strips, newsprint, meter stick, pin hole, laser, screen, 35mm slide frame, clamp/ring stand slide holder, masking tape, plastic ruler, machinist's scale. I. SIMULATED DOUBLE SLIT INTERFERENCE When a portion of a wavefront from a source strikes two openings in a barrier, new wavefronts are launched on the far side of the barrier (Fig. 1). These new sources S 1 and S 2 send out identical, in-phase wavefronts in the shape of half-circles toward the observation screen. The amplitudes of these waves add to one another algebraically to produce an interference pattern. In the locations on the screen for which a crest from S 1 and S 2 both arrive at the same time, constructive interference occurs. The same thing happens where troughs from both sources arrive at the same time. The net result is that the waves reinforce one another. At these locations the crests (and troughs) are twice as large (and twice as deep) as either wave alone. In the locations on the screen for which a crest from S 1 and a trough from S 2 both arrive at the same time, destructive interference occurs. The same thing happens where troughs from S 1 and crests from S 2 arrive at the same time. The net result is that the waves cancel one another. There is no net wave at all at these locations. We will find the locations of constructive and destructive interference in a simulated double slit interference experiment using wave strips. Physics 116 Interference and Diffraction Dr. Richard Feinberg Spring 2014 Page 1.
Figure 1. Double Slit Interference. a. To simulate the waves coming from S 1 and S 2, pin the reinforced end of each strip to a piece of cardboard covered by a piece of drawing paper (Fig.2). Use a separation d = 10 cm between the pins. Make sure the wave on each strip has the same amplitude and phase at the pin. Connect the pins with a line (i.e., make them both crests). Figure 2. Simulated Double Slit Interference. b. Draw a straight line perpendicular to the line between the pins and equidistant from each pin. This is the central axis. Draw another straight line perpendicular to this one a distance L = 50 cm away from the line joining the pins. This will simulate the location of the screen on which the waves will interfere. Page 2 Physics 116 Interference and Diffraction Dr. Richard Feinberg Spring 2014.
c. Slide the wave strips over one another, keeping them crossed at the screen. Mark the positions on the screen where a crest from one wave strip exactly intersects the crest of the other wave strip (e.g. point A in Fig. 2). This is where constructive interference is taking place and interference maxima are located. d. Mark the positions on the screen where a crest from one wave strip exactly intersects the trough of the other wave strip (e.g. point B in Fig. 2). This is where destructive interference is taking place and interference minima are located. It can be shown that the positions of the maxima and minima on the screen are given by: Maxima: y Bright L tan m and sin Bright d Bright Minima: ydark L tan Dark ( m 1 ) and sin Dark 2 d where m = 0, ±1, ±2, ±3,... e. Measure the distances of your maxima and minima from the central axis to get y Bright and y Dark. Fill in the tables below. f. Use the formulas for y Bright and y Dark to solve for the wavelength of the wavestrips for each data point. MAXIMA MINIMA m y Britght (cm) (cm) m y Dark (cm) (cm) 1 0 2 1-1 -1-2 -2 g. Average of all values of = h. Measure the wavelength directly from one of the strips. It is more accurate to measure the length of say five complete waves and divide the result by 5. Directly measured value of = Percent difference between the two methods (from Parts g. and h.) = Physics 116 Interference and Diffraction Dr. Richard Feinberg Spring 2014 Page 3.
II. DIFFRACTION 1. Diffraction by a Small Pinhole When light passes through a small aperture like a slit or pinhole, it does not cast an exact shadow of the hole. Instead, it diffracts (spreads out). Since Huygens Principle tells us that each point on the wavefront passing through the aperture acts like a new source of spherical waves, these waves will spread out and interfere with one another on a screen placed some distance away. The result is a pattern of maxima and minima even if just one aperture is used. It is called the single slit diffraction pattern or the single hole diffraction pattern depending on which type of aperture is used. a. Clip the 2 X2 piece of gray plastic into the binding clip mounted on a ring stand. This piece of plastic has a second piece of thin plastic glued to it that has a very small circular aperture that has been burned with a carbon dioxide laser. b. Move the pinhole in front of the laser until light passes through the pinhole and falls on a screen a few meters away. c. If the pinhole is reasonably round, you should see a series of concentric rings (Fig. 3). Make a sketch of your observations here. Figure 3. Pinhole Diffraction. d. What would happen to the pattern if the hole is made larger? Do not really do this! Touching the pinhole will degrade its ability to produce a clean, circular pattern! Page 4 Physics 116 Interference and Diffraction Dr. Richard Feinberg Spring 2014.
III. APPLICATIONS 1. Measuring the Diameter of a Human Hair It can be shown from diffraction theory that an obstacle placed in a coherent beam produces a diffraction pattern that is identical to a slit of the same size. So the diffraction pattern from a slender obstacle like a hair should produce the same pattern as a single slit (Fig. 4). a. Tape a hair into an empty film slide frame and place it in a laser beam. Observe the "single slit" diffraction pattern that develops perpendicular to the direction of the hair. b. Measure the locations of the diffraction minima (dark spots) from the central axis and fill in the data table Figure 4. Single Slit Diffraction. c. Recall that the locations of the minima of the single slit diffraction pattern where destructive interference occurs are given by sin m m 1, 2, 3,... a The wavelength of our Helium-Neon laser is 633 nm (1 nm = 1 10-9 m) For small angles, we can use the approximation sin = tan = = Y m /L and simplify this to Y m m L a Solve for the diameter of the hair "a" and complete the data table. m Y m (cm) a(cm) +3 +2 +1-1 -2-3 d. Average value of hair diameter a =. Physics 116 Interference and Diffraction Dr. Richard Feinberg Spring 2014 Page 5.
2. Measuring the Wavelength of Light with a Ruler! When light reflects off a mirror-like surface diffraction can occur from any bumps or depressions present. We will use a steel machinist s scale as a "reflection grating". The lines on the scale are etched into the metal and make excellent, regularly spaced depressions to produce a diffraction pattern. a. Set up a laser to strike the surface of the scale at a glancing angle (very large angle of incidence with respect to the normal) so that it produces a streak of light about 1" long. Observe the reflected light on a screen about 2-3 meters away (Fig. 5). Figure 5. Laser Beam Reflected From a Scale. b. When the laser beam strikes a flat, unetched surface of the scale, it acts like an ordinary mirror and produces a single reflected spot on the screen. Mark this spot on your screen as Y 0. It is the location of the specular reflection. c. Now slide the scale over until the laser beam strikes the finest divisions etched on the scale. This is the edge with very fine lines labeled 100 ths. The separation d between adjacent lines is 0.010". d. You should see a series of diffracted spots above the Y 0 spot previously marked and maybe one spot below it. Mark these spots and label them as indicated in the diagram. e. Measure the heights of the Y's relative to the height of the ruler's surface and fill in the data table. m Y m (cm) (cm) 0 ------------------- 1 2 3 Page 6 Physics 116 Interference and Diffraction Dr. Richard Feinberg Spring 2014.
f. The location of the m th diffraction spot Y m can be used to calculate the wavelength of light from the formula 2 2) d ( Ym Y0 2 2m L where d = groove spacing on the scale L = distance from center of laser streak on scale to screen m = order number of diffraction spot ( 0, 1, 2,...) Y m = height of the m th diffraction spot above the ruler's surface g. Average of all values of = = nanometers (nm) Percent difference between the above result and the accepted value of 633 nm = h. Observe the diffraction pattern produced by a coarser scale. Explain any differences between this pattern and the one produced by the 100 ths scale. Physics 116 Interference and Diffraction Dr. Richard Feinberg Spring 2014 Page 7.