LC-1: Interference and Diffraction

Transcription

1 Your TA will use this sheet to score your lab. It is to be turned in at the end of lab. You must use complete sentences and clearly explain your reasoning to receive full credit. The lab setup has been changed slightly since the lab manual has been written. The light source is now a laser diode, with a wavelength of 635 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. 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). 5) An optical track on which all these pieces can be mounted. A. Interference: Start out with Experiment II in the lab manual In your setup, you will be doing 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. 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 (1.0 m from the detector), and the laser diode directly behind it (this barely fits on the track). 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. 1

2 A2) The wavelength of the diode laser is about 635 nm. Calculate 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 DataStudio by double-clicking on the settings file LC-1_IntDiff.ds on the desktop. Use the computer to record the intensity pattern: click start and slowly moving the photodetector across the interference pattern by turning the wheel. Enlarge the data so only the central peak and two peaks to the left fill the screen. Record the distances between the central maximum and the neighboring max. and min. From central peak to neighbor peak From central peak to nearest minimum 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 d x + d /2 L 2

3 A6) Calculate on your calculator 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. Distance from right slit (m) # wavelengths in this distance Distance from left slit (m) # wavelengths in this distance Difference in distances # wavelengths in this difference Peak next to central peak Minimum next to central peak A7) The waves from each slit start out in phase, and they propagate difference distances. What is the condition that they interfere constructively/destructively? Compare to your data. 3

4 A8) The annoyance in A6) is that you are subtracting two numbers that are both close to 1 m, and 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 mathematically it is tied up in the square root. An expansion that we commonly use in physics gets around this: ( 1+ ") 1/ 2 #1+ " /2 where δ is a very small number << 1. Show on your calculator over what range this is a good approximation. δ 1+δ ( 1+ ") 1/ 2 1+δ/2 Error There are higher order terms in the expansion, but as you can see we often don t need them. A9) Show that the difference in distances can be written as xd /L by using the approximate relation of A8) with your result of A5). Verify that the approximation is valid. Hint: factor out an L 2 from inside the square root to make it of the form 1+ " ( ) 1/ 2 4

5 A9) Plot distance from the central maximum of several secondary maxima and minima of interference pattern obtained in part A4). Find an equation that fits the graph. Compare to theory of A8. Dist from central peak (cm) Max or Min # (e.g. first peak away from center, first min away from center) A10) Put the white screen back up in front of the detector, and rotate the variable double slit in front of the laser beam. The slit separation in this pattern varies from mm to 0.75 mm. Describe how the maxima separations change with slit width, and compare to the results of A8. 5

6 B. Diffraction: Experiment 1 in your lab manual Take out the Multiple slit set wheel and put the Diffraction set in front of the laser diode. Turn the wheel to put the 0.08 mm width single-slit diffraction slit in the laser beam. Put the white screen in front of the photodetector and turn the laser on. B1) Describe/draw what you see on the white screen. B2) Why do you see maxima and minima in the experiment (Hint: remember Huygen s principle, that each portion of the slit acts as a source of spherical light waves). B3) Remove the white screen and use the computer to collect intensity vs position. Plot the minima and maxima positions as a function of position as for two-slit interference. What relation describes this data? Dist from central peak Max or Min # (e.g. 1, 2,3) 6

7 B4) Use the computer to record intensity vs position for all four different single-slits. In the space below, write some words that summarize the general trend of the intensity pattern as the diffraction slit changes width. B5) From your data, find a mathematical relation between the width of the central peak (distance between minima on either side of it) and the slit width. Slit Width Central peak width Mathematical relation 7

8 B6) With the help of the picture below, find the phase shift between a wave originating at the bottom of the slit, and one originating a distance z up from the bottom of the slit. x z L θ z zsinθ = path length difference Need to add up all the Huygens spherical waves emanating from each point along the slit The form of each wave at point x on the screen is sin("t + #) where " is a phase shift that is related to the path length difference and the wavelength. Phase shift = 8

9 B7) The amplitude of the light at point x on the screen is the sum of all spherical waves emanating from different parts on the slit. In the space below, add up all the waves by integrating the wave amplitude over z from d/2 to +d/2. The intensity is the square of this. 9