Practice Problems for Chapter 25-26 1. What are coherent waves? 2. Describe diffraction grating 3. What are interference fringes? 4. What does monochromatic light mean? 5. What does the Rayleigh Criterion state? 6. If the distance between fringes decreases, what is happening to the space between the slits? 7. What is the difference between a virtual and a real image? 8. An object produces a virtual image in a concave mirror. Where is the object located? 9. Why are convex mirrors used as rearview mirrors? 10. Explain how an eye works. 11. What happens to an image in the eye? 12. What factor, other than the curvature of the surfaces of the lens, determines the location of the focal point? 13. Why is using monochromatic light important regarding Young s experiment? 14. Why is the diffraction of sound waves more familiar in every day life compared to that of light waves? 15. Why do diffraction gratings have large numbers of grooves? Why are the grooves so close together? 16. Explain why a central bright line produced when light is diffracted by a double slit cannot be used to measure the wavelength? 17. Describe how you could use light of a known wavelength to find the distance between two slits. 18. As the wavelength of the light decreases, what can be said about it s interference pattern?
19. If a beam of light reaches a point through a slit one wavelength behind another beam of light, what is observed on the screen? 1. A concave mirror has a radius of curvature of 20.0 cm. An object, 2.0 cm high, is placed 30.0 cm from the mirror. A) Where is the object located? B) How high is the image? 2. An object, 2.0 cm high, is placed 5.0 cm in front of a concave mirror with a focal length of 10.0 cm. How large is the image and where is it located? 3. A convex security mirror in a warehouse has a radius of curvature of 1.0 m. A 2.0 m high forklift is 5.0 m from the mirror. What is the location and size of the image? 4. An object is placed 32.0 cm from a convex lens that has a focal length of 8.0 cm. A)Where is the image? B) If the object is 3.0 cm high, how high is the image? C) Is the inverted or erect? 5. A convex lens with a focal length of 6.0 cm is held 4.0 cm from an insect that is 0.50 cm long. A) Where is the image located? B) How large does the insect appear? 6. A two-slit experiment is performed to measure the wavelength of red light. The slits are 0.0190 mm apart. A screen is placed 0.600 m away and the separation between the central bright line and the first-order bright line is found to be 21.1 mm. What is the wavelength of the red light? 7. Two narrow slits separated by 0.40 mm are illuminated by monochromatic light of wavelength 500 nm. How many bright fringes can be seen on a screen 1.0 cm wide placed 1.0 m in front of the slits? 8. A monochromatic plane wave is normally incident on a diffraction grating with 1.00 x 105 lines/m. For what visible wavelengths would this grating produce a maxi- mum at theta= 10.0 degrees? 9. Find the position of the first minimum for a single slit of width 0.04 millimeters on a screen 2 meters distant, when light from a He-Ne laser λ = 632.8 nm is shone on the slit. 10. If a car is approaching you at night with headlights 1 meter apart, how far away must you be in order to just resolve them? (treat the headlights as single slits of width 1 millimeter, and assume the lamps are monochromatic sodium sources of wavelength 589.29 nm). 1. Can two points 10 4 mm apart be resolved with a light microscope?
2. A microscope objective with a magnification of 10 is used in a microscope with a magnification of 50. Find the focal length of the ocular if the ocular s image is formed at the eye s near point, 25 cm from the eye. Neglect the distance between the eye and the ocular. 3. A CO2 laser produces infrared radiation with a wave- length of 10.6 um and a bandwidth of 106-5 nm. What is the coherence length of the radiation? 4. In the double-slit interference pattern, what is seen is the interference of the diffracted waves produced by each of the slits. The brightest fringes are those that correspond to the central diffraction maximum of each slit. Suppose that each of the slits is 0.200 mm wide, the slits centers are 0.900 mm apart, and they are illuminated by a source of wavelength 600 nm. How many bright fringes will be seen in the central maximum? 5. The surface of a compact disk (CD) behaves as a kind of diffraction grating. When light is reflected from the sur- face, each of the closely spaced ridges on a CD behaves as the source of a spherical light wave. Except for the fact that light is reflected rather than transmitted, the effect is the same as for the transmission gratings described in the text; that is, one sees a spectrum of colors (Fig. 26 30). Suppose a beam of sunlight is normally incident on a CD. You see yellow light of wavelength 575 nm reflected at an angle of 30.0 degrees relative to the normal. Find the number of ridges per mm on the CD.
Answers to 25-26 3. Waves that are in phase. They have the same wavelength, velocity, and frequency. 7. A device that with parallel divisions that reflect light and form an interference pattern. 8. Pattern of dark and light bands on a screen due to consecutive and destructive interference of light waves passing through two narrow, closely spaced slits. 11. It is light with only one wavelength. 5. As you move farther from two light sources, the sources appear to resolve. 6. They are increasing. 7. Real images can be projected onto a screen or seen on a piece of paper. A virtual image cannot be seen on a screen or paper. 8. Between the focal point and the mirror. 9. Because convex mirrors enlarge the field of view. 11. Light passes through the cornea and pupil (lenses). The iris (muscle) controls how much light can pass through. There are rods on the back of the eye that reads the image and then it is sent through the optic nerve. 11. The image is actually inverted because your eye is a convex lens and somehow through your nerves and brain, the image appears erect. 12. The refractive index of the lens material. 13. Because in order to make sure that there are not too many variables, having a monochromatic light source means that coherent waves are formed. 14. Because sound waves have much larger wavelengths so their diffraction is much more obvious. If a band is playing in a building as you pass by an open door than you hear the music before you see the band. 15. Because diffraction pattern of one line alone would not produce enough intensity to be seen by itself. But when diffracted light from thousands of lines interference, brightness, sharp diffraction maxima are produced. 16. Because regardless of the wavelength of the light, when it hits the middle bright spot it is the same distance for all so lengths interact constructively.
17. Because we know the formula of = xd/l 18. The distance between the maxima decreases. 19. Bright fringe. 1. A- real and inverted. B- -1.0 cm. 2. 4.0 cm and virtual/erect 3. 0.18 m, erect, virtual, smaller 4. A-Virtual.B- -1.0cm high. C-Inverted 5. A- real. B- 1.5 cm upright 6. 668 mm 7. 9 8. 580 nm, 435 nm 9. 3.16 cm 10. L= 1.70 x 10^3 m 1. No 2. 6.3 cm 3. 1.12 x 10^4 m 4. 9 5. 870