Unformatted text preview: Light/Wave Interference Objective: To see how light waves interfere constructively and destructively. To observe interference and diffraction. To measure small apertures or objects using their diffraction patterns. Apparatus: Laser, slides (singleslit, doubleslit, diffraction grating), slide holder clip and stand assembly, small projection screen with white paper, meter stick Introduction Diffraction is the phenomenon whereby light "bends" when it encounters an obstacle. Because light has wavelike properties, the diffracted light may interfere with itself which can result in interesting and complex patterns of bright and dark regions (in the case of visible light). The interference can be constructive (bright areas) or destructive (dark areas) depending on the path difference between the diffracted light waves. If the path difference is such that the diffracted waves arrive in phase, there will be constructive interference. If the diffracted waves arrive out of phase, there will be destructive interference. In today's lab you'll study three different situations in which light diffraction and interference occur. Specifically, you'll study the interference patterns that occur when laser light is incident on a single slit opening, a double slit opening, and a diffraction grating. Single Slit Consider laser light that is incident on a single slit opening. The diffracted light that exits the slit will result in the interference pattern shown below. Notice there are many bright areas (maxima in light intensity) and many dark areas (minima in light intensity). The positions of the minima are given by the following expression: b sin = m ; m=1,2,3,. .. Here b is the width of the single slit, is the angular deflection (as measured from the central maximum) of the minima on a screen far away, is the wavelength of the incoming light and m is the order of the minimum. The higher order minima are farther from the central maximum; positive minima are above (to the right of) the central maximum, while negative minima are below (to the left of) the central maximum. See the diagram below: You will find singleslit diffraction to be useful in determining the sizes of very small objects. For example, you can determine the width of the slit using the single slit interference equation (assuming you know all other quantities, of course). What if you don't have a slit, but you instead have an opaque object whose size you'd like to know? For small objects, you can use the same equation if you employ what is called Babinet's principle  the diffraction pattern for a slit is the same as the pattern for an opaque object of the same shape illuminated in the same manner. That is, except for the intensity of the central spot, the interference pattern produced by a slit of arbitrary shape is the same that would be produced by an opaque object of the same shape. Double Slit Now consider laser light that is incident on two closely spaced slits that are parallel to one another. The diffracted light that exits the two slits will result in the interference pattern shown below. Notice that the pattern is similar to but not the same as the single slit interference pattern. The positions of the interference maxima are given by the following expression: d sin = m ; m=0,1,2,3,... Here d is the distance between the slits, is the angular deflection of the bright areas (maxima) on a screen far away, is the wavelength of the incoming light and m is the order of the maximum. Note that the above diagram shows an idealized double slit, which ignores the single slit character of each of the two single slits. A true double slit would exhibit closely spaced dark and light areas (fringes), superimposed over the single slit pattern The single slit profile is said to modulate the double slit pattern, as shown below: Diffraction Grating Now consider light that is incident on a diffraction grating. (A diffraction grating contains many closely spaced, parallel slits.) The diffracted light that exits the grating will result in the interference pattern shown below. The interference pattern will contain very sharp, bright spots where the positions of these maxima are given by the following expression: d sin = m ; m=0,1,2,3,... The equation here looks the same as for the double slit case, except that d represents the distance between grating lines. (You will have to calculate this from the table on the next page, which lists lines per unit distance.) The situation is still very similar to the double slit because there are many lines interfering constructively; the resulting interference pattern is therefore very sharp. Clockwise from top left  Single Slit, Double Slit, Diffraction Grating SLIDE SPECIFICATIONS Single Slit slide: PATTERNS NO. SLITS SLIT WIDTH Double Slit slide: PATTERN NO. SLITS SLIT WIDTH SLIT SPACE Diffraction Gratings: A 2 .04 mm .250 mm B 2 .04 mm .500 mm C 2 .08 mm .250 mm D 2 .08 mm .500 mm A 1 .02 mm B 1 .04 mm C 1 .08 mm D 1 .16 mm 80, 100, 300, and 600 lines/mm. Calculate d, the distance between lines. Activities You will use a human hair (which one lab partner will provide) and three slides (single slit, double slit, diffraction grating to investigate interference and diffraction. Measuring the distance from the slide to the screen and the distance from the central maximum to the maximum or minimum in question will give you the angle with some calculation; remember that you can utilize small angle approximations only if the distance from the slide to the screen is large compared to the distance from the minimum/maximum to the central maximum. A. Single Slit Devise an experiment to measure the wavelength of the laser light using a single slit. Use at least two single slits of different widths and average your results. Note that in the equation, the only unknown variable is while the other variables are known or measurable. Remember that the equation gives the positions of the minima. B. Double Slit Devise an experiment to measure the wavelength of the laser light using a double slit. Use at least two double slits of different spacings and average your results. Note that in the equation, the only unknown variable is while the other variables are known or measurable. Remember that the equation gives the positions of the maxima and that you should measure the distances between the small dark areas inside the single slit envelope, not the largespaced distances between the single slit envelope minima. C. Diffraction Grating Devise an experiment to measure the wavelength of the laser light using a diffraction grating. Use at least two diffraction gratings of different spacings and average your results. Note that in the equation, the only unknown variable is while the other variables are known or measurable. Remember that the equation gives the positions of the maxima and that d is the spacing between grating lines. D. Measure the thickness of a human hair Devise an experiment to measure the thickness of a human hair. You or your one of your lab partners will have to provide the hair. Explain how your experiment will measure the thickness and show all your calculations (Think about Babinet's principle). You will need the wavelength you determined previously. ...
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 Spring '09
 rollino
 Physics, Diffraction, Light, Wavelength, Diffraction grating, single slit, Babinet

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