LC-1: Interference Name_____________________________ Lab #1 Worksheet Section___________ 1 Your TA will use this sheet to score your lab. You need to turn it in at the end of lab. You must use complete sentences and clearly explain your reasoning to receive full credit. The lab setup for this lab has been changed slightly since the lab manual has been written. The light source is now a laser diode, with a wavelength of 660 nm. The same handling precautions apply to this as for the He-Ne laser discussed in the manual: the laser diode is a source of extremely intense light, which can damage your or someone else’s vision if mishandled. Please look over the section about laser safety in the lab manual. Your experiment consists of 1) A laser diode light source, 2) A circular wheel of single slits of various widths, 3) A circular wheel of double slits of various widths and spacings, 4) A light detector. The light detector also has a circular wheel in front of it, with slits of various larger widths. You move the light detector perpendicular to the beam path to quantitatively measure intensity variations of the interfering or diffracted light. The different slits are to set the spatial resolution of the light detector: slit #1 works well, with a sensitivity setting of “10” (slide switch on detector). If this is too sensitive (so that the detector saturates, as evidenced by flat tops to the diffraction peaks), you can use “1”. 5) An optical track on which all these pieces can be mounted. A. Interference: Start out with Experiment II in the lab manual Here you will be investigating two-slit interference. The two slits illuminated by the laser beam act as two sources of spherical waves of light that are of the same frequency and same phase. These spherical waves form an interference pattern throughout all space. That is, at all points in space, the total light is a superposition of light originating from the two slits. You investigate the interference pattern visually by looking at the reflection from a white screen, and you record quantitative information on the computer with a light detector that you move manually across the interference pattern. Setup: Put the white screen on the track in front of the light detector, position the “Multiple slit set” circular wheel at 110 cm on the track, and the laser diode directly behind it (this barely fits on the track). Make sure that the circular disc lines up with the 110 cm mark, and not just some part of the plastic holder. This sets the slit-screen distance to 100 cm. Turn the multiple slit wheel to position the “a=0.04 mm, d=0.25 mm” double slit in front of the laser beam. A1) Describe or sketch what you see on the white screen.LC-1: Interference Name_____________________________ Lab #1 Worksheet Section___________ 2 A2) The wavelength of the diode laser is about 670 nm. Calculate approximately how many wavelengths of laser light are in the space between the slits and the white screen. A4) Now take off the white screen, and start the DataStudio program on the lab computer by clicking once on the settings file on the “Laboratories” page of the course web site. Use the computer to record the intensity pattern: click start and slowly move the photodetector across the interference pattern by turning the wheel. Enlarge the data in DataStudio so only the central peak and two peaks on either side fill the screen. Record the distances between the central maximum and the immediately adjacent minimum, and the closest maximum. From central peak to nearest minimum From central peak to neighbor peak A5) Use the Pythagorean theorem to write expressions for the distances from the two slits to a point on the screen a distance x from the central maximum. Use L for the screen distance, and d for the slit separation. ! x + d /2 ! x " d /2 d L Detector Slits xLC-1: Interference Name_____________________________ Lab #1 Worksheet Section___________ 3 A6) Using A5, calculate the numerical values of the distances from each slit to the detector position for the points measured in part A4), and the differences between them. Be careful in this calculation to keep enough digits. You may need to subtract 100 cm from the value displayed on your calculator in order to see enough digits. Peak next to central peak Valley next to central peak Distance from right slit (cm) # wavelengths in this distance Distance from left slit (cm) # wavelengths in this distance Difference in distances # wavelengths in this difference A7) The waves from each slit start out in phase, but they propagate difference distances to reach the same spot at the detector. What is the condition that they interfere constructively? Destructively? How does this compare with the results in your table above?LC-1: Interference Name_____________________________ Lab #1 Worksheet Section___________ 4 A8) In A6) you subtracted two numbers (distance from left and right slits) that are both close to 1 m, different from each other by only a few wavelengths of light. You would think that it would be possible to somehow cancel out the 1 m, since it is common to both, but it is tied up in the square root. A bit of mathematical magic we commonly use in physics is the binomial expansion, which in its simplest form is ! 1+"( )1/ 2# 1+"/2 . This is a good approximation when δ is a small number much less 1. Use your calculator to complete the following table. This demonstrates the range of δ over which this is a good approximation. δ 1+δ ! 1+"( )1/ 2 1+δ/2 % Error 0.01 1.01 0.10 1.10 0.500 1.500 A9) Here we apply ! 1+"( )1/ 2# 1+"/2 to the differences in path lengths from the two slits as determined in A5. The difference in path lengths can be calculated as ! L2+ x + d /2( )2( )1/ 2distance from left slit to position x on screen1 2 4 4 4 3 4 4 4 " L2+ x " d /2( )2( )1/ 2distance from right slit to position x on screen1 2 4 4 4 3 4 4 4 = path length differenceL2+ x2+ xd + d2/ 4( )1/ 2" L2+ x2" xd + d2/ 4( )1/ 2= L2+ x2( )1/ 21+ d x + d / 4( )/ L2+ x2( )( )1/ 2" 1+ d "x + d / 4( )/ L2+ x2( )( )1/ 2# $ % & ' ( ) L2+ x2( )1/ 21+12d x + d / 4( )/ L2+ x2( )* + , - . / "12L 1+ d "x + d / 4( )/ L2+ x2( )( )= xd / L2+ x2( )1/ 2= path length difference This is the path length difference as
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