Stevens High School AP Physics II Work for Not-school

Transcription

1 1. Gravitational waves are ripples in the fabric of space-time (more on this in the next unit) that travel at the speed of light (c = 3.00 x 10 8 m/s). In 2016, the LIGO (Laser Interferometry Gravitational Wave Observatory) detected gravitational waves produced by merging black holes with a frequency peaking at 256 Hz. What was the approximate wavelength of the gravitational waves observed? a x 10-7 m b. 7.8 x 10 5 m c x 10 6 m d. There is insufficient information to answer 2. Light from a source that produces a single frequency passes through a single slit A. The diffraction pattern on a screen is observed. Slit A is then replaced by slit B, and the new pattern is observed to have fringes that are more closely spaced than those in the first pattern. Which of the following is a possible explanation for why the spacings are different? a. Slit A is wider than slit B. b. Slit B is wider than slit A. c. The distance between the light source and the slit is greater for slit A than for slit B. d. The distance between the light source and the slit is greater for slit B than for slit A. 3. Students in a lab group are given a plastic block with a hollow space in the middle, as shown in the figures above. The index of refraction n p of the plastic is known. The hollow space is filled with a gas, and the students are asked to collect the data needed to find the index of refraction n G of the gas. The arrow represents a light beam that they shine into the plastic. They take the following set of measurements: The three measurements are shared with a second lab group. Can the second group determine a value of n G from only this data? a. Yes, because they have information about the beam in air and in the plastic above the gas. b. Yes, because they have information about the beam on both sides of the gas. c. No, because they need additional information to determine the angle of the beam in the gas. d. No, because they do not have multiple data points to analyze. Page 1

2 4. A driver is backing a car off of a lawn into a driveway while using the side-view mirror to check for obstacles. The figure above shows a top view of the car and some objects near the car. The mirror is a plane mirror, and the dashed line shows the angle of its plane. Using a straightedge, determine which of the following the driver should be able to see in the mirror just by turning her head at the position shown? Select the best two answers. a. Herself b. The tree c. The mailbox d. The utility pole The following 5 questions ask you to sketch ray diagrams. Please use a straightedge when you do, and indicate the image properties in each case (real/virtual, upright/inverted, enlarged/reduced). 5. Sketch a ray diagram for an object located 15 cm from a concave mirror with a focal length of 6 cm. 6. Sketch a ray diagram for an object located 10 cm from a convex mirror with a focal length of 12 cm. 7. Sketch a ray diagram for an object located 20 cm from a spherical converging lens with a focal length of 30 cm. 8. Sketch a ray diagram for an object located 5 cm from a spherical diverging lens with a focal length of 8 cm. 9. You have two spherical mirrors: Mirror A is convex with R = 30 cm, and the other is concave with R = 20 cm. Which of the following can produce an upright, enlarged image (real or virtual)? a. Placing the object 10 cm in front of mirror A b. Placing the object 20 cm in front of mirror A c. Placing the object 35 sm in front of mirror A d. Placing the object 5 cm in front of mirror B e. Placing the object 15 cm in front of mirror B Page 2

3 10. In which case is total internal reflection possible? a. If light passes from a material with high index of refraction to low index of refraction. b. If light passes from a material with low index of refraction to high index of refraction. c. Either case is possible. d. Neither case is possible. 11. The separated colors of a rainbow are caused by which optical phenomenon? a. Reflection b. Dispersion c. Refraction d. Diffraction 12. Let s say you have a magnifying glass (n G = 1.55) and you use it to focus the Sun s rays to a point (useful for starting fires). This point is located at the focal point of the lens, 12 away from it in air (where the index of refraction is 1.00). If the same lens was used to focus light in water (where the index of refraction is 1.333), would the point at which the rays focus be: a. The same b. More than 12 from the lens c. Less than 12 from the lens d. The lens would become a diverging lens so its focal length would be negative e. The lens would no longer have a focal point. 13. Light with a wavelength of 600 nm in air passes into glass which has an index of refraction of If the frequency of light is constant, what is the wavelength of the light in the glass? a. 600 nm b. 500 nm c. 400 nm d. 300 nm e. None of the above 14. Light falls onto a double-slit, and the second-order bright fringe is found to be 2.1 mm from the centerline of the diffraction pattern. Remember, the central maximum is called the 0 th order, the next bright peak is the 1 st order, etc. What is the width of the central maximum? a mm b mm c mm d mm 15. A red laser is used to produce a single-slit diffraction pattern with a certain spacing. If a green laser is used with the same slit width as before, which of the following correctly describes the new diffraction pattern? a. The fringes will be more closely spaced b. The fringes will be the same distance apart c. The fringes will be farther apart d. No diffraction pattern will be formed. Page 3

4 16. A circular coil of wire is in the plane of the page with a clockwise current flowing in it as shown. A negatively charged particle passes just over the top of the coil. Which of the following paths best represents the trajectory of the particle? 17. In each of the following 4 cases, a negatively charged particle moves with a velocity, v, in a magnetic field, B, as shown. What is the direction of the magnetic force in each case? 18. Which one of the following curves best illustrates the shape of an isobaric process for a fixed amount of an ideal gas? 19. Some students experimenting with an uncharged metal sphere want to give the sphere a net charge using a charged aluminum rod. Which of the following steps would give the sphere a net charge of the same sign as the rod? a. Bringing the rod close to, but not touching the metal sphere, then moving the rod away. b. Bringing the rod close to, but not touching the metal sphere, then momentarily touching a grounding wire to the metal sphere. c. Bringing the rod close to, but not touching the metal sphere, then momentarily touching a grounding wire to the rod. d. Touching the rod to the sphere. Page 4

5 1. A beam of light is incident on a double-layer of glass and plastic as shown ( a = 45 o ). a. Sketch the path of the transmitted and reflected rays in the material, making sure that your angles are qualitatively correct. b. Now, using Snell s Law, calculate the angle of refraction in the glass and plastic. c. Finally, you should have two reflected beams which reach the bottom of the slab. One reflected beam comes from the plastic-glass interface, and the other reflected beam comes from the airplastic interface and then refracts as it passes into the glass. How far apart are these two exiting rays of light (measured along the bottom of the slab)? 2. While scuba diving, you pause an look up toward the surface of the water from a depth of 12 m as shown. The sum appears to be at the apparent position shown, but your eyes are being tricked by refraction. The actual position of the Sun is actually closer to the horizon (and the rays bend toward your eye as they enter the water). a. Using the information provided in the sketch, determine the angle of the beam of light in the water. b. Determine the angle of incidence for the Sun s rays in the air. Remember, Snell s Law requires that you measure your angles from normal or perpendicular to the boundary. c. What is the difference between the apparent position and the actual position of the Sun in terms of the angle,. d. As the sun sets, what is the angle of refraction in the water? Page 5

6 3. An object is placed 10 cm in front of a converging lens with a focal length of 30 cm. a. Draw a ray diagram and determine the approximate location of the image b. Use the lens equation to calculate the position of the image and check that it agrees with your answer to part a). c. What is the magnification of the image? d. Describe the image properties: real/virtual, enlarged/reduced, upright/inverted. 4. An object is placed somewhere between the focal point and center of curvature of a concave mirror with a focal length of 1.6 m. Remember, this means that the center of curvature will be at 2R = 3.2 m. a. Draw a ray diagram and determine the approximate location of the image b. Given that the image formed is real and is located at si = 4.8 m, calculate the object location. c. What is the magnification of the image? d. Describe the image properties: real/virtual, enlarged/reduced, upright/inverted 5. An equilateral prism is used to slit the spectrum of light present in white light (I only show the blue and red beams). The indices of refraction for these two colors of light are given in the sketch. Determine the angular separation (labeled in the diagram) for these two colors of light. 6. A single slit is used to form a diffraction patter as shown. The wavelength, slit width, and length are given: a. Determine the angle shown in the diagram,. b. Determine the value of x o. c. Determine the value of x. Page 6

7 7. A double slit is used to form a diffraction pattern as shown. The wavelength, slit separation, and distance between the slits and screen (not shown in the diagram, but it is 1.50 m) are as shown: a. What is the angular position of the m = 1 bright spot (measured with respect to the central maximum at m = 0)? b. What is the total distance labeled x in the diagram (the distance from the m = -2 peak to the m = 2 peak)? 8. You have a lens constructed as shown. One side of the lens is flat, and the other side has a radius of curvature, R. The index of refraction of the glass is n g = 1.5. a. Derive an expression for the angle of incidence ( g in the figure) in terms of the horizontal position that the beam strikes the curved side (x). I have provided the angle for the spherical arc of the glass to assist you. Show that, when x = 0.98 m, g = o. b. For the values provided in part (a), show that = 17.4 o. c. Determine the value of x* (shown in the diagram) based on these numbers. You have now found a focal point of the lens! d. Repeat the calculations you did in steps a-c for another beam which strikes the curved side of the glass at x = 0.99 m. You should find that x* is nearly the same as you did in part c. Page 7

8 e. Qualitatively speaking, if you submerged the lens in water, how would the location of x* change? Would it get closer to the lens, farther from the lens, or stay in the position shown? Why? f. Qualitatively speaking, if the radius of curvature of the lens increases (the lens becomes less curves), will x* shift in position? Where will it move? 9. (Challenge): Rainbows are pretty (pretty dang geometrically fun, that is and just plain pretty, too). Here s a little picture of how they are formed (which I drew fairly carefully to help you. For an angle of incidence of = 60 o for white sunlight (I know, I used a red pen for it), show that the angle = 42.4 o. This is the angle between the Sun s rays and the rainbow s position, which is why they are only visible in specific circumstances. Page 8