Diffraction and Interference of Light Theory: When light encounters an opaque barrier with an opening that is not too large relative to the wavelength, it will bend around the edges to illuminate the space behind the opening as if the opening is a source of light itself. The flaring of the light around barriers is called diffraction. Geometric optics (ray tracing) does not predict diffraction. If light traveled only in lines, a small slit would show a sharp shadow. However, if light is wavelike in nature it will diffract at an aperture and interfere at a distance from the aperture. In this experiment, you will demonstrate that light can be made to diffract and interfere and thus has a wavelike nature. A. Fraunhofer Diffraction from a Single Slit. If a parallel beam of monochromatic light falls on an opaque plate having a narrow vertical slit, and is then observed on a screen sufficiently distant from the slit so that the light rays are essentially parallel, an effect called Fraunhofer diffraction is observed. What is observed is sketched in Figure 6-1. The light on the screen is a central bright band, wider than the slit with alternating dark and bright bands of decreasing intensity, as shown in Figure 6-2. The angle, at which the first dark ban will occur, was derived by Fraunhofer to be D 1 Figure 6-1, n = 1, 2,... [1] where a is the slit width and the angle to the nth dark band is given by different values of n. The wavelength of the light is and must be in the same units as a. The form of equation [1] is a hint that interference is taking place, and can be derived by noting x Figure 6-2
that interference will occur between light passing through different parts of the slit. If the angle θ is small, the sine function will be very close to the tangent function and the equation [1] can be expressed as. [2] B. Interference of light from Two Slits. If a beam of monochromatic light falls on two very narrow slits that are close together, the light will appear to come from two sources that are related. In figure 6-3a if S 1 and S 2 are the two sources, the waves from each will add in phase at the points where the curved lines cross to give a bright situation. When the light falls on the screen there will be regions of constructive interference (bright) and destructive interference (dark) as shown in Figure 6-4. The first bright fringes on either side of the central bright fringe are called 1 st order. Successive fringes are given order numbers that identify their position relative to the central fringe. The set up shown in Figure 6-3b allows one to calculate the angle between the m th fringe and the central fringe. sinθ m = [3] where d is the separation between the slits. Using the geometry of Figure 6-3b and y as the distance of the mth fringe as shown in Figure 6-4, equation [3] becomes Figure 6-4 [4] D S 1 S 1 d S 2 S 2 m y (a) Figure 6-3 (b)
Procedure: Zero Fringe y What will be referred to as the detection assembly should already be assembled. It consists of the linear translator, the rotary motion sensor, the light sensor and the aperture bracket. The light sensor needs to be plugged into socket A and the rotary motion sensor into Channel 1 (yellow) and 2 on the Pasco Interface box. The rotary motion sensor should be able to move freely back and forth along the linear translator. When making measurements this device will perform two tasks simultaneously. As the light sensor is moved along the linear translator it will measure the light intensity entering the sensors and the rotary motion sensor will measure the distance traveled along the horizontal of its motion. Preliminary Setup 1. Turn on the computer and open the file diffraction in the 1402 folder 2. Place the laser at the opposite end of the track from the detection assembly. Move the light sensor/aperture bracket on the detection assembly so that it is aligned along the center of the optical rail. Have a lab partner press the back of the rotational motion sensor down. Turn on the laser and adjust the thumbscrews on the back of the laser so that the spot is in the middle of the aperture slit on the detection assembly (see Figure below).
Single Slit 1. On the table, you have two sets of apertures. Locate the Single Slit Set and adjust it so that the 0.04 single slit is centered in the middle of the hole. Place the aperture mount into the optical rail close to the laser with the single slit selector facing towards the detection assembly. Make necessary adjustment to the laser so that the beam passes through the slit and a diffraction pattern (see figure below) forms on the detection assembly. You want the intensity of this pattern to be at its brightest and also to be horizontal to the aperture. This may include loosening the brass screw and moving the single slit selector within the mount. 2. To start, set the aperture on the detection assembly to 4 and the gain switch on the light sensor to x10. Measure the distance, D, from the single slit aperture to the aperture on the detection assembly. Record the value onto data sheet 1. 3. Move the light sensor/aperture on the detection assembly to one side. Then select RECord from the DAQ window on the computer. Then slowly and steadily pull or push the light sensor/aperture on the detection assembly through the diffraction pattern. Select STOP from the DAQ window after you have moved completely through the pattern.
4. Select the graph display and then choose the Auto Zoom Button. If necessary use the Magnify button then click and drag over the region of interest to expand that region. You should have a graph that should resemble figure 6 2. The pattern shown is intensity vs. position. IMPORTANT INFORMATION: READ You may have to experiment to obtain a suitable pattern to make your measurements. By either decreasing or increasing the gain on the light sensor or by change the aperture on the detection assembly or a combination of the two. There is no set procedure to obtain the desired pattern since each setup is different and dependent on the alignment of the laser, the power of the laser etc. 5. On the graph, consider the dark bands to be in sets of pairs. The first set would be the first valleys (minimum intensity) on either side of the central peak and therefore would be the first order. Each subsequent pair increases the order number and the distance from the central peak. Using the Analyze Tool measure the position of the first order, m=1, dark bands to the right and left of the central peak. Record the displayed value for the position of the dark band; do not bother at this peak. time to determine its distance from the central 6. Determine the average position of the dark band from the peak, x, using (Right position left position)/2. Then using equation [2] and your measured and given values, calculate the slit width, a, and enter the value into the data table. Note: When doing calculations, it may be best to first convert all values to meters. Then once the result is calculated convert meters to the units asked for in the final result. 7. Repeat the above steps for the second order, m = 2, using the second dark band from the central maximum peak. Record the values into the data table. Lastly, find the average slit width for the two orders. 8. Adjust the Single Slit aperture to the 0.08 position, and repeat the above steps to complete the data table. 9. Position the Single Slit aperture to the variable slit, and rotate through the slit from the large to small slit. Observe the pattern that is produced and answer the questions on the data sheet for the single slit. Double Slit 1. Remove the single slit aperture and replace with the Multi Slit aperture. Adjust the aperture so that the double slit (a = 0.04, d = 0.25 is in the center of the hole). With the laser on, view the interference pattern created on the detection
assembly. Readjust the laser using the thumbscrews to align the beam so that it passes through the center of the two slits. Make the necessary adjustments to obtain a bright horizontal pattern as shown below. 2. On the detection assembly set the aperture to 3 and the light sensor to x10. Measure and record the distance between the double slit aperture and the aperture in front of the light sensor. Record this value as D, on data sheet 2. 3. Move the light sensor/aperture to one side of the detection assembly and select RECord on the DAQ window. Slowly move the light sensor through the interference pattern, then select STOP on the DAQ window when finished. Use the magnify button and select the central region where the strongest multiple peaks are located. If the peaks are difficult to distinguish, you will have to try a different setting, either adjust the aperture (i.e. 2 or 4) or change the gain settings on the light sensor (see tip box in the prior procedure). 4. In determining the slit spacing, we are concerned with the position of the bright spots, or peaks, in relation to the central maximum peak. Once a measurable pattern is obtained on the computer screen select the analyze tool in the graph display window and use it to measure the position of the first order bright spot (peak) to the right and left of the central maximum peak. Record the values into the data table. Determine the average distance between the central peak and the first order peak, y. It should be understood that y is simply used as a variable, and does not represent the vertical component of the graph. Using equation [4], calculate the spacing between the slits, d. 5. Repeat step 4 for the second order bright spots. 6. Adjust the Multiple Slit aperture to the variable double slit with its largest slit spacing. While observing, the interference pattern, rotate the slit to its smallest slit spacing. Answer the question on the data sheet.
Data Sheet 1 Single Slit Measurements Diffraction of Light Distance between single slit and aperture slit, D = 0.1 cm Wavelength, = 670 10 nm nm = 10-9 m Slit 0.04 (mm) Order Position of dark bands x (cm) calculated m Left (cm) Right (cm) (Right-Left)/2 slit width a (mm) 1 2 1 2 Slit 0.08 (mm) Average Slit width Average Slit width Show calculations below using the second order for each slit width. How does your result compare to the given values for the slit width? What happens to the diffraction patter as the slit width increases?
Data Sheet 2 Double Slit Interference of light Distance between single slit and aperture slit, D = 0.1 cm Wavelength, = 670 10 nm Slit 0.04 (mm) Spacing 0.25 (mm) Order Position of bright spots y (cm) calculated m Left (cm) Right (cm) (Right-Left)/2 spacing between slits, d (mm) 1 2 Show calculations below Average Slit spacing How does your result compare to the given values for the slit spacing? What happens to the diffraction patter as the distance between the slits increases?