Current Score: 0/20. Due: Tue Apr :15 PM EDT. Question Points. 0/1 0/1 0/3 0/3 0/1 0/3 0/2 0/2 0/2 0/2 Total 0/20.

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1 1 of 8 4/10/2010 3:38 PM Current Score: 0/20 Due: Tue Apr :15 PM EDT Question Points /1 0/1 0/3 0/3 0/1 0/3 0/2 0/2 0/2 0/2 Total 0/20 Description This assignment is worth 20 points. Each part is worth 1 point. Assume the numbers given in each problem are accurate to three significant figures. WebAssign expects your answers to be accurate within 1%. If you don't round off until the end, and then round off to three significant figures, you should be fine. Occasionally there are errors in WebAssign. If you are convinced your answer is correct and WebAssign is grading you incorrectly please check with Professor Duffy. 1. 0/1 pointsduffy_ep_ch24_p101 [ ]

2 2 of 8 4/10/2010 3:38 PM he picture above shows a source of light (the red dot), with the light shining on the origin, which is marked by the position of the reen dot. The horizontal axis is the interface separating one medium from another. Some of the light reflects back into the first edium, and some refracts into the second medium. hoose the three correct statements about this situation from the list below. The first medium (where the source is) has a higher index of refraction than the second medium. The first medium has the same index of refraction as the second medium. The first medium has a lower index of refraction than the second medium. If the index of refraction of the second medium was increased, the angle of the reflected beam would change. Changing the index of refraction of the second medium would have no effect on the angle of the reflected beam. If the light source was moved to the position of the purple dot in the second medium, and the light was incident on the origin again, the light would definitely experience total internal reflection. If the light source was moved to the position of the purple dot in the second medium, and the light was incident on the origin again, some light would refract out into the upper medium, traveling toward the position of the red dot. If the light source was moved to the position of the purple dot in the second medium, and the light was incident on the origin again, some light would refract out into the upper medium, but the light would not travel toward the position of the red dot. 2. 0/1 pointsduffy_ep_ch24_p102 [ ] The picture above shows a source of light in the lower medium (the purple dot), with the light shining on the origin, which is marked by the position of the green dot. The horizontal axis is the interface separating one medium from another. In this case, all of the light reflects back into the lower medium.

3 3 of 8 4/10/2010 3:38 PM hoose all the correct statements about this situation from the list below. The lower medium (where the source is) has a larger index of refraction than the upper medium. The lower medium has the same index of refraction as the upper medium. The lower medium has a smaller index of refraction than the upper medium. The angle of incidence in this case is greater than the critical angle for total internal reflection to occur. The angle of incidence in this case is smaller than the critical angle for total internal reflection to occur. If the light source was moved to the position of the red dot in the upper medium, and the light was incident on the origin again, the light would definitely experience total internal reflection. If the light source was moved to the position of the red dot in the upper medium, and the light was incident on the origin again, some light would refract into the lower medium, traveling toward the position of the purple dot. If the light source was moved to the position of the red dot in the upper medium, and the light was incident on the origin again, some light would refract into the lower medium, but the light would not travel toward the position of the purple dot. 3. 0/3 pointsduffy_ep_ch24_p103 [ ] This picture shows a light source at point A, at the top left of the picture. The light which refracts into the lower medium eventually reaches point B, at the bottom right of the picture. Point A is located at x = 0 m, y = +5 m, and point B is located at x = +10 m, y = -5 m. The upper medium is air, with an index of refraction of n = The interface separating the two media lies along the line y = 0. Take the speed of light in vacuum to be 3.00 x 10 8 m/s. An interesting fact about light is that the path it takes from A to B always minimizes the total light travel time. In other words, any other path from A to B, including the shortest-distance path, would take the light more time. One can show that this is equivalent to Snell's law. In the case shown in the picture, the time it takes the light to travel from point A to the green point, on the interface, is 27.0 ns. By using Snell's law and considering the geometry, answer the following.

4 4 of 8 4/10/2010 3:38 PM a) What is the x-coordinate of the green point? = 6.37 m b) What is the index of refraction of the second medium? 1.34 c) What is the total time, in nanoseconds, it takes the light to travel from point A to point B? 54.6 ns 4. 0/3 pointsduffy_ep_ch24_p20_alt [ ] A lamp emitting red light is placed at the bottom of a tank of liquid with depth H = 20.0 cm and index of refraction n = 1.65 (for red light). Above the liquid is air, which has an index of refraction of On the surface of the liquid above the light, an observer sees a bright circle with radius R. (a) Why does the observer see a bright circle on the surface? Because the lamp is circular. Because the pupils in the observer's eyes are circular. Because light striking the surface outside of the circle experiences total internal reflection. (b) Calculate the radius of the bright circle seen by the observer cm c) From the list below, choose the two correct statements. The first three statements relate to light that travels from the lamp toward oint A, along the solid line in the figure. The other three statements relate to what happens when the lamp emits green light instead f red light. Note that the index of refraction of this liquid decreases as the wavelength of light increases - this is true for most aterials. If a beam of light travels directly from the lamp to the surface at point A, it refracts out into the air and goes away infinitely far from the lamp. If a beam of light travels directly from the lamp to the surface at point A, it goes away infinitely far from the lamp along the surface of the liquid. If a beam of light travels directly from the lamp to the surface at point A, it reflects back into the liquid. If the lamp is adjusted to emit green light instead, the radius of the bright circle decreases. If the lamp is adjusted to emit green light instead, the radius of the bright circle stays the same.

5 5 of 8 4/10/2010 3:38 PM If the lamp is adjusted to emit green light instead, the radius of the bright circle increases. 5. 0/1 pointsduffy_ep_ch24_p30 [ ] Binoculars generally use pairs of prisms in which the light experiences total internal reflection. Each prism (in blue on the diagram) is right-angled, with the other two angles being 45. A diagram of the path followed by light as it travels through the prisms to your eyes is shown in the figure above. If the prisms are surrounded by air, determine the minimum index of refraction of the prism material /3 pointsduffy_ep_ch24_p40 [ ] As shown in the figure above, a beam of red and violet light is incident along the normal to one surface of a right-angled triangular glass prism. The glass has an index of refraction of 1.52 for red light, and 1.54 for violet light. The prism is surrounded by air, which has an index of refraction of Note that you will probably find it helpful to draw a sketch showing how the red and violet beams travel from the point at which they enter the prism to the side ab of the prism. (a) If the angle at vertex a of the prism is = 28.0 degrees, determine the angles of refraction for the red and violet beams that merge from the prism from the side ab. Show these refracted beams on your sketch. The angles of refraction are measured, as sual, from the normal to the surface. ngle of refraction for the red light is 45.5 degrees angle of refraction for the violet light is 46.3 degrees b) What is the smallest index of refraction the prism could have for light to experience total internal reflection when it is first incident n the side ab, for the geometry described above? Assume the light enters the prism as in the diagram /2 pointsduffy_ep_ch21_p102 [ ] wo speakers, which are separated by a distance d = 4.00 m, produce sound waves with the same amplitude, phase and frequency. ou stand a distance of 4.50 m directly in front of the left speaker, on the dashed line shown in the diagram.

6 6 of 8 4/10/2010 3:38 PM (a) Assume the speed of sound to be 340 m/s. What is the lowest frequency the sound can have to produce completely constructive interference at your location? 224 Hz b) What is the lowest frequency the sound can have to produce completely destructive interference at your location? 112 Hz 8. 0/2 pointsduffy_ep_ch21_p06_alt [ ] wo identical speakers are pointed at one another, along the x-axis. The speakers, which are in phase with one another, broadcast dentical sound waves at a frequency of 170 Hz. Assume the speed of sound to be 340 m/s. Speaker A is positioned at x = 0, and peaker B is located at x = m. a) In between the speakers, there are a few locations at which the two waves produce completely destructive interference. What is he x-coordinate of the point closest to speaker B at which completely destructive interference occurs? 9.6 m b) In between the speakers, there are also a few locations at which the two waves produce completely constructive interference. How any locations are there, along the line between the speakers, at which completely constructive interference occurs? 11 locations. 0/2 pointsduffy_ep_ch25_p102 [ ]

7 7 of 8 4/10/2010 3:38 PM The pattern above is produced by interference between identical waves emitted by two sources. Red denotes positive displacement of the medium, while blue denotes negative displacement. Black indicates zero displacement. At the orange point near the top, we say that constructive interference is occurring. The distance the orange point is from the left source is the length of the purple line; the distance the orange point is from the right source is the length of the green line. (a) Select all the true statements about this situation. For constructive interference to occur at the orange point, the net displacement must be non-zero at all times at that point. For constructive interference to occur at the orange point, the distance from each source to the orange point must be an integer number of wavelengths. For constructive interference to occur at the orange point, the path-length difference for the orange point must be an integer number of wavelengths. The path-length difference is the distance the point is from the left source minus the distance the point is from the right source. In this particular case, the orange point is two wavelengths farther from the left source than it is from the right source. b) In this case, what is the distance between the two sources, in terms of wavelengths? 5 wavelengths 10. 0/2 pointsduffy_ep_ch25_p103 [ ]

8 8 of 8 4/10/2010 3:38 PM The pattern above is produced by interference between identical waves emitted by two sources. Red denotes positive displacement of the medium, while blue denotes negative displacement. Black indicates zero displacement. At the orange point near the top, we say that destructive interference is occurring. The distance the orange point is from the left source is the length of the purple line; the distance the orange point is from the right source is the length of the green line. (a) Select all the true statements about this situation. Because the orange point is in a region of destructive interference, the net displacement at the orange point is zero at all times. For destructive interference to occur at the orange point, the distance from each source to the orange point must be an integer number of wavelengths plus half a wavelength. For destructive interference to occur at the orange point, the path-length difference for the orange point must be an integer number of wavelengths plus half a wavelength. The path-length difference is the distance the point is from one source minus the distance the point is from the other source. In this particular case, the orange point is 1.5 wavelengths farther from the left source than it is from the right source. b) In this case, the sources are separated by a distance of 50.0 cm, and the distance the orange point is from the source on the right s 82.0 cm. How far is the orange point from the source on the left? 67 cm Assignment Details