G3 TWO-SOURCE INTERFERENCE OF WAVES
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1 G3 TWO-SOURCE INTERFERENCE OF WAVES G4 DIFFRACTION GRATINGS HW/Study Packet Required: READ Tsokos, pp SL/HL Supplemental: Hamper, pp DO Questions pp #1,3,8,9,10 REMEMBER TO. Work through all of the example problems in the texts as you are reading them Refer to the IB Physics Guide for details on what you need to know about this topic Refer to the Study Guides for suggested exercises to do each night First try to do these problems using only what is provided to you from the IB Data Booklet Refer to the solutions/key ONLY after you have attempted the problems to the best of your ability UNIT OUTLINE I. TWO-SOURCE INTERFERENCE OF WAVES A. INTERFERENCE PATTERNS FROM TWO SOURCES B. YOUNG S TWO-SLIT EXPERIMENT II. DIFFRACTION GRATINGS A. MULTIPLE SLIT DIFFRACTION B. DIFFRACTION GRATINGS FROM THE IB DATA BOOKLET WHAT YOU SHOULD BE ABLE TO DO AT THE END OF THIS TOPIC State the conditions necessary to observe interference between two sources Explain the interference pattern produced by waves from 2 coherent point sources Appreciate the meaning of the terms coherence and coherent sources Define and recognize phase difference and path difference Describe a two-slit experiment and draw the resulting intensity distribution pattern Understand and apply formulae for two-source interference State the effect on the intensity of light by adding more narrow slits with the same separation Derive the diffraction grating formula for normal incidence Outline the use of the diffraction grating to measure wavelengths of light Solve problems with the diffraction grating formula 1
2 HOMEWORK PROBLEMS: 1. A double slit is arranged so that its plane is normal to a beam of laser light, as shown below. The wavelength of the light is 640 nm. The slit separation in the double slit arrangement is 0.85 mm. Coherent light emerges from the slits and an interference pattern is observed on a screen. The screen is parallel to the plane of the double slits. The distance between the slits and the screen is 2.4 m. a) State what is meant by coherent light. b) Explain how an interference pattern is formed on the screen. c) Calculate the separation of the fringes in the interference pattern on the screen. [ m] d) The interference pattern in (b) consists of a series of alternate light and dark fringes. The intensity of the light from one slit is now reduced. Suggest the effect on the appearance of the fringes. 2
3 2. Light from a laser is incident on two very narrow slits A and B (diagram not to scale). Point C on the screen is directly opposite the midpoint of the slits. a) On the axes below, sketch the variation with angle θ of the intensity of the light on the screen. b) The separation of the slits is mm and the wavelength of the light is m. The distance between the slits and the screen is 1.40 m. Calculate the separation of the bright fringes on the screen. [7.93 mm] c) Slit A is covered with a transparent piece of glass. The effect of the glass is to increase the path length of the light from the slit to the screen by half a wavelength. It may be assumed that the amount of light absorbed by the glass is negligible. State and explain the effect(s), if any, of the glass on the i) intensity pattern you have drawn in (a). ii) separation of the bright fringes calculated in (b). 3
4 3. Monochromatic, coherent light is incident on two narrow parallel slits whose widths are small compared to their separation. After passing through the slits the light is brought to a focus on a screen producing interference fringes. Point X is the midpoint of the slits. a) The angular position of a point on the screen is determined by the angle θ. i) Explain why the intensity of light at θ = 0 will be a maximum. ii) The wavelength of light is m and the separation of the slits is m. Show that for the first order maximum θ = rad. iii) On the axes below draw a graph to show how the intensity of light observed on the screen varies with angle θ. (You do not have to put numbers on the vertical axis.) b) The two slits are replaced by a large number of slits whose widths and separation are the same as in (a). State the changes, if any, in the intensity pattern you drew in (a)(iii) with reference to i) the value of the intensity at θ = 0. ii) the angular position of the points of maximum intensity. iii) the angular width of the fringes. 4
5 4. Light from a laser is incident on two identical parallel slits whose width is small compared to their separation (diagram not to scale). a) After passing through the slits the light is incident on a screen. The separation of the slits is 0.50 mm and the distance between slits and screen is 2.0 m. The wavelength of the light is 700 nm. i) Determine the separation of points of maximum intensity on the screen. [2.8 mm] ii) Describe the effect that increasing the number of slits would have on the intensity pattern on the screen. b) The slits in (a) are replaced with a diffraction grating that has lines per metre. Determine the number of positions of maximum intensity that will be observed on the screen. [ 9] 5
6 5. Light from a laser is incident on two slits of equal width. After passing through the slits, the light is incident on a screen. The diagram below shows the intensity distribution of the light on the screen. a) The wavelength of the light from the laser is 633 nm and the angular separation of the bright fringes on the screen is 4.00 x 10-4 rad. Calculate the separation of the slits. [1.58 mm] b) Light from the laser is incident on many slits of the same width as the widths of the slits above. Draw, on the above diagram, a possible new intensity distribution of the light on the screen. c) The laser is replaced by a source of white light. Describe, if any, the changes to the fringes on the screen. 6
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