PAGE 1/13 Exp. #2-7 : Measurement of the Characteristics of the Light Interference by Using Double Slits and a Computer Interface Measurement of the Light Wavelength and the Index of Refraction of the Air by Using a Michelson Interferometer Student ID Major Name Team No. Experiment Lecturer Student's Mentioned Items Experiment Class Date Submission Time Submission Place Introductory Physics Office Report Box # Students should write down Student s Mentioned Items at the cover page of Experiment Reports, and then complete Experiment Reports by adding contents to the attached papers (if needed) in terms of the following sections. Contents of the reports should be written by hand, not by a word processor. Instead, it is allowed that figures and tables are copied and attached to papers. Completed Experiment Reports should be submitted to the place due to the time specified by Experiment Lecturers. The Experiment Report score per each Experiment Class is evaluated by max. 50 points (basically 15 points). Solutions of Problems in Experiment Reports are not announced to the public according to the General Physics Laboratory - Administration Rule. If a student permits other students to pirate one s Experiment Reports or a student pirates Experiment Reports of other students regardless of permission of original creators, the corresponding Experiment Report score and Active Participation score will be zero in case of exposure of such situation. Unless Experiment Reports are submitted to the place due to the time specified by Experiment Lecturers, the corresponding Experiment Report score will be zero. If the submission rate of Experiment Reports is less than or equal to two thirds, the grade of General Physics Laboratory will be F level. In order to decide grades of General Physics Laboratory at the end of current semester, the detailed scores of General Physics Laboratory will be announced at Introductory Physics Office homepage. Based on the announcement, students can raise opposition of score error. Since the public evidence is needed for the confirmation of opposition, students should keep one s Experiment Reports completed evaluation by Experiment Lecturers until the Experiment Report score decision If a student is absent from the Experiment Class because of proper causes, the corresponding student should submit documents related to absence causes to Introductory Physics Office regardless of cause occurrence time until the grade decision of General Physics Laboratory. If a student moves the Experiment Class arbitrarily without permission of Introductory Physics Office, it is noted that the total Experiment Scores will be zero. Lecturer's Mentioned Items Submission Time/Place Check Experiment Report Points Evaluation Completion Sign 50
PAGE 2/13 1. Objective Student ID Name A. Measurement of the Characteristics of the Light Interference by Using Double Slits and a Computer Interface : For the interference phenomena due to a double slit, the relation among the dimension of a double slit, the interference pattern and diffraction pattern will be understood. B. Measurement of the Light Wavelength and the Index of Refraction of the Air by Using a Michelson Interferometer : The light wavelength and the index of refraction of the air will be measured by using a Michelson interferometer. In addition, the Michelson-Morley's experiment will be demonstrated qualitatively whether the light propagates through a medium called ether or not. 2. Theory A. Measurement of the Characteristics of the Light Interference by Using Double Slits and a Computer Interface (1) Interference due to a double slit Let us consider the interference phenomena due to a double slit as shown in Fig. 1. Since the relation sin tan can be approximately made for a sufficiently small angle, the path difference is given as follows: (Eq. 2) Here, is the distance between two slits in a double slit, is the distance between the double slit and the screen, and is the distance between the considered point and the center on the screen. If the path difference is equal to half the light wavelength multiplied by even numbers, bright fringes representing the constructive interference with maximum light intensity appear on the screen. On the other hand, if the path difference is equal to half the light wavelength multiplied by odd numbers, dark fringes representing the destructive interference with minimum light intensity appear on the screen. < Maxima of the interference pattern > ( : integer) (Eq. 3) < Minima of the interference pattern > ( : integer) (Eq. 4) Fig. 1. Interference due to a double slit. This experiment supports the fact that light has a wave property. When Young performed the optical interference experiment in 1801, a single slit was placed between a light source and a double slit. Since a laser as a light source is used nowadays, a single slit is not used. This means that a single slit transforms incoherent light into coherent light causing the interference phenomena. Laser is an abbreviation of "light amplification by stimulated emissive radiation". Therefore, an intrinsically coherent laser causes the interference phenomena without a single slit. The light incident on a double slit passes through slits and to cause the interference phenomena. Assuming that the screen is located sufficiently far from the double slit, the path difference of two lights is given by sin. (Eq. 1) Let us find the separation of the interference pattern, that is, the distance between adjacent maxima or minima on the screen. Since the difference of integers corresponding to adjacent maxima or minima is, the separation of the interference pattern is given by,. (Eq. 5) By using this result, the light wavelength can be found from the separation of the interference pattern. Answer the following questions. 1. In general, the sunlight cannot cause the interference phenomena without a single slit. Explain why the sunlight is incoherent light.
PAGE 3/13 (2) Diffraction due to a single slit Let us consider the diffraction phenomena due to a single slit as shown in Fig. 2. Let us find the separation of the diffraction pattern, that is, the distance between adjacent maxima or minima on the screen. Since the difference of integers corresponding to adjacent maxima or minima is, the separation of the diffraction pattern is given by,. (Eq. 9) Note that the width of the central maxima is given by. (3) Light intensity by a double slit Since a double slit usually used has the single-slit width smaller than the slit separation, the separation of the diffraction pattern is greater than that of the interference pattern. In the double-slit experiment, both the interference and diffraction patterns can be simultaneously observed. The pattern with small separation corresponds to the interference pattern and the diffraction pattern acts like an envelope for the interference pattern as shown in Fig. 3. It is known that the light intensities in the interference and diffraction patterns are proportional to cos sin and, respectively. Here, and are given as follows: sin, sin (Eq. 10) Therefore, the light intensity in the double-slit experiment is proportional to cos sin. For the case of and, a sufficiently number of interference fringes are located on the central maxima of the diffraction pattern so that the interference pattern can be easily observed regardless of the diffraction pattern. Fig. 2. Diffraction due to a single slit. Let us divide the space in a single slit with a width by even numbers. Assuming that the screen is located sufficiently far from a single slit, if the path difference between the lights passing the divided regions is equal to half the light wavelength, minium light intensity can be observed on the screen. This result can be expressed into a formula as the following. sin, sin ( : nonzero integer) (Eq. 6) Since the relation sin tan can be approximately made for a sufficiently small angle, the condition for the diffraction minima is given as the following. < Minima of the diffraction pattern > sin ( : nonzero integer) (Eq. 7) Assuming the diffraction maxima is located near the midpoint between adjacent diffraction minima, the condition for the diffraction maxima is given as the following. < Maxima of the diffraction pattern > sin ( : integer) (Eq. 8) Fig. 3. Light intensity in the double-slit experiment.
PAGE 4/13 B. Measurement of the Light Wavelength and the Index of Refraction of the Air by Using a Michelson Interferometer (1) Michelson-Morley's experiment There was a tendency to emphasize the wave property of the light excessively in the end of 19th century. The waves usually experienced needs the medium in order to propagate. However, the question about the medium for the light remained. Michelson-Morley's experiment was performed in order to detect the medium for the light called "ether". In the Michelson-Morley's experiment, a Michelson interferometer with the structure as shown in Fig. 4 was used. In a Michelson interferometer, two lights divided by a semi-transparent mirror acting as a beam splitter make a round trip by the distances and and then interfere with each other. In a Michelson interferometer, the path difference between two lights making a round trip by the distances and is, and the condition for the constructive interference is given by, (Eq. 12) where is the light wavelength and is an integer. (i) While one of the distances or is changed by, the path difference is changed by. If interference fringes are observed during the change, the light wavelength is given as follows:, (Eq. 13) (ii) When a material with the width is placed in the middle of one of the distances or, the path difference is changed by, where is the difference of the index of refraction in the space with and without a material. If interference fringes are observed during the change, the difference of the index of refraction is given as follows:, (Eq. 14) If a Michelson interferometer is located in the air and the material is vacuum, the index of refraction of the air is given as follows:, (Eq. 15) Fig. 4. Michelson interferometer. When the Earth is rotating around the Sun in the space filled with ether, ether moves with the speed equal to the orbital speed of the Earth in the reference Answer the following questions. 2. Investigate other interference phenomena such as thin film and Newton s ring. frame fixed in the Earth. Assume that the directions of the distances and are perpendicular and parallel to the orbital velocity of the Earth, respectively. The durations for the light to make a round trip by the distances and given by, (Eq. 11) are different, where is the light speed observed in the reference frame at rest. Therefore, it was predicted that the interference fringes can be observed for the case of. Surprisingly, the interference fringes were not observed in the Michelson-Morley's experiment, which means that ether does not exist. That is, the light can propagate without the medium and the speed of the light is a constant in any reference frame, which provides one of the postulates in the Einstein's special theory of relativity. (2) Michelson interferometer In spite of the result of the Michelson-Morley's experiment, a Michelson interferometer is still used in various measurements. Michelson himself showed that m corresponds to times the wavelength of the red light emitted in the cadmium (Cd) light source by using a Michelson interferometer. This measurement result made him win a Nobel prize in 1907 and provided the basis for the standard of meter (m ) as the unit of length adopted in 1961.
PAGE 5/13 3. Experimental Instruments A. Measurement of the Characteristics of the Light Interference by Using Double Slits and a Computer Interface Items Quantity Usage Clean up method Computer 1 set It is used to acquire and analyze data. It should be placed at the center of the experiment table. Sensor shift driver (Computer interface) 1 set It is used to measure the light intensity. It should be placed at the center of the experiment table. USB/power connection cable 1 ea. It is used to connect the computer/wall power to the sensor shift driver. It should be mounted at the sensor shift driver. Optic sensor 1 ea. It is used to measure the light intensity. Laser 1 ea. It is used as a light source. Laser power adaptor 1 ea. It is used to connect the laser to the wall power. Viewing screen 1 ea. It is used to view the propagation path of the light. Diffraction plate 1 ea. It is used to interfere and diffract the light. Tape measure 1 ea. It is used to measure the distance between the laser and the screen. Optical table 1 ea. A laser is placed on the optical table. It should be mounted at the sensor shift driver. It should be placed at the center of the experiment table.
PAGE 6/13 < How to Use the Sensor Shift Driver > [1] Connect the computer/wall power to the USB/power connection terminal located at the back face of the sensor shift driver. Connect the magnetic./optic sensor mounted at the sensor shift driver to the magnetic/optic sensor connection terminal located at the back face of the sensor shift driver. [2] After turning on the computer, open the SensorLab program. After selecting Motor Driver as a device, click the Connect button of the SensorLab program. [3] Sensor shift speed selection switch located at the front face of the sensor shift driver can be set to one of Low Mid High positions, and sensor shift direction selection switch located at the front face of the sensor shift driver can be set to one of Left 0 Right positions. By using these switches and the SensorLab window, place the sensor at the center of the measuring object. If the above procedure is completed, place the sensor at the one edge of the sensor shift driver again. [4] Magnetic sensor range/optic sensor selection switch located at the top face of the sensor shift driver can be set to one of 5G 50G 500G OPT positions, and zero adjustment knob (ZERO ADJ) located at the top face of the sensor shift driver can be adjusted. By using these switches and the SensorLab window, adjust the zero status. [5] Set the sensor shift speed selection switch to the proper position. Start the sensor shift by using the sensor shift direction selection switch, and click the Start button of the SensorLab program to start the measurement. Check if the acquired data is displayed in the screen. [6] If the data is acquired, stop the sensor shift by using the sensor shift direction selection switch, and click the Stop button of the SensorLab program to stop the measurement. Repeat this procedure to acquire the correct data. [7] Save the data in the computer by selecting File Save ******.txt in the menu of the SensorLab program and copy the text files to a USB memory prepared beforehand. [8] After the experiment is finished, close the SensorLab program and turn off the computer. Clean up the experimental instruments according to the suggested method.
PAGE 7/13 B. Measurement of the Light Wavelength and the Index of Refraction of the Air by Using a Michelson Interferometer Items Quantity Usage Clean up method Michelson interferometer 1 set It is used to interfere the light and measure the light wavelength and the index of refraction of the air. It should be placed at the center of the experiment table. Laser 1 ea. It is used as a light source. Laser power adaptor 1 ea. It is used to connect the laser to the wall power. It should be placed within the box at the center of It should be placed within the box at the center of Convex lens 1 ea. It is attached to a Michelson interferometer in order to expand the laser spots. Vacuum hand pump + Chamber 1 ea. It is used to measure the index of refraction of the air. Scale 1 ea. It is used to measure the width of the chamber.
PAGE 8/13 4. Experimental Procedures A. Measurement of the Characteristics of the Light Interference by Using Double Slits and a Computer Interface (1) Connect the computer/wall power to the USB/power connection terminal of the sensor shift driver. After turning on the computer, open the SensorLab program. After selecting Motor Driver as a device, click the Connect button of the SensorLab program. (2) Place the laser with known light wavelength sufficiently far from the optic sensor acting as the screen. Use a tape measure to measure the distance between the laser and the screen. (3) By using the sensor shift speed/direction selection switch and the SensorLab window, place the optic sensor at the center toward the laser. Use the optical table for height adjustment of the laser. If the above procedure is completed, place the optic sensor at the position slightly away from the center again. (4) Place the locations D, E, and J of the diffraction plate in front of the laser. Use the viewing screen to view the propagation path of the light. Note that the laser light should not be directly incident to one's eyes. (8) Measure the separation of the interference pattern and the width of the central maxima of the diffraction pattern in the data. Calculate the slit separation and the single-slit width, and compare them with the reference values. While changing the slit separation and the single-slit width, observe the change of the fringes and interpret the meaning of the observed results in terms of the interference and diffraction patterns. (9) If the measurement is finished, clean up the experimental instruments according to the suggested method. B. Measurement of the Light Wavelength and the Index of Refraction of the Air by Using a Michelson Interferometer (1) Measurement of the light wavelength & (2) Measurement of the index of refraction of the air 1) Use the surface of the wall as the screen and place a Michelson interferometer sufficiently far from the screen. Place a laser beside the Michelson interferometer and turn on the laser. Control the position of the laser and the angle of the semi-transparent mirror of the Michelson interferometer so that two laser spots appear close to each other on the screen. Attach a convex lens to the Michelson interferometer in order to expand the laser spots. Note that the laser light should not be directly incident to one's eyes and the convex lens should not be lost. Rotate the horizontal and vertical shift screws in the Michelson interferometer so that the interference fringes appear with a circular shape. Note that the screw with a spring in the Michelson interferometer should not be controlled. (5) Set the optic sensor selection switch and the sensor shift speed selection switch to OPT position and Low position, respectively. Start the sensor shift by using the sensor shift direction selection switch, and click the Start button of the SensorLab program to start the measurement. Check if the acquired data is displayed in the screen. (6) If the data is acquired, stop the sensor shift by using the sensor shift direction selection switch, and click the Stop button of the SensorLab program to stop the measurement. Repeat this procedure to acquire the correct data. (7) Save the data in the computer by selecting File Save ******.txt in the menu of the SensorLab program and copy the text files to a USB memory prepared beforehand.
PAGE 9/13 2) Set the scale of the micrometer in the Michelson interferometer to the origin. After rotating the micrometer to change the fringes with the number of,, and, measure the number of changed scales of the micrometer. Considering that the one scale of the micrometer is m and the shift distance of a mirror connected to a micrometer is times the shift distance of the micrometer in the present model of a Michelson interferometer, calculate the light wavelength and compare it with the reference value. 3) Place a chamber attaching a vacuum hand pump in the Michelson interferometer, and rotate the horizontal and vertical shift screws in the Michelson interferometer so that the interference fringes appear again. Fix the chamber by one's finger if the chamber is not placed tightly. After removing the air in the chamber by using a vacuum hand pump, restore the air in the chamber and count the number of changed fringes. Note that the vacuum hand pump should not be broken by applying excessive force. Use a scale to measure the width of the chamber. Calculate the difference of the index of refraction between the air and vacuum from the light wavelength obtained in (2), and compare it with the reference value. 4) If the measurement is finished, clean up the experimental instruments according to the suggested method.
PAGE 10/13 5. Experimental Values A. Measurement of the Characteristics of the Light Interference by Using Double Slits and a Computer Interface Light wavelength of the laser (nm) Distance between the double slit and the screen (cm) Diffraction plate Observed fringes Location D Location E Location J Diffraction plate Separation of the interference pattern (mm) Reference value (mm) Slit separation Experimental value (mm) Error (%) Width of the central maxima of the diffraction pattern (mm) Reference value (mm) Single-slit width Experimental value (mm) Error (%) Location D Location E Location J
PAGE 11/13 B. Measurement of the Light Wavelength and the Index of Refraction of the Air by Using a Michelson Interferometer (1) Measurement of the light wavelength # of changed fringes Shift distance of the mirror (m ) (m ) = # of changed scales of the micrometer m Slope m -intercept -intercept m Reference value Experimental value Error Light wavelength (nm) (nm) (%) (2) Measurement of the index of refraction of the air Width of the chamber (mm) Experimental value of the light wavelength obtained in (1) (nm) # of changed fringes #1 #2 #3 Average Difference of the index of refraction between the air and vacuum Difference of the index of refraction Reference value Experimental value Error (%) between the air and vacuum (, atm)
PAGE 12/13 6. Results and Discussions (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents should be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report is allowed.) Write down contents in terms of the following key points. 1. Explain the relation between the separation of the interference pattern and the slit separation, while the single-slit width keeps constant. 2. Explain the relation between the width of the central maxima of the diffraction pattern and the single-slit width, while the slit separation keeps constant. 3. Discuss the usefulness of the Michelson interferometer measuring the light wavelength and the index of refraction of the air.
PAGE 13/13 7. Solution of Problems (This page should be used as the first page of the corresponding section. If the contents exceed this page, additional contents should be written by attaching papers. Contents should be written by hand, and not by a word processor. Attaching copied figures and tables to the report is allowed.) 8. Reference