More problems for midterm 2 and final PDF

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More problems for midterm 2 and final...

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General Physics with Calculus (PH212) Fall Term 2014 Some Random, Miscellaneous Review Problems for the Second and Final Exams Below are a few more practice problems, some of which have appeared on previous physics exams at OSU and LBCC. These problems are in no way inclusive of every possible problem or topic that could appear on the exam. The number of problems per topic presented here is in no way reflective of the percentage of that topic that will appear on the exam. It is nearly certain that not one of these will show up on the next exam. They are simply for more exposure and practice. Knowing how to do these on your own suggests you understand some things but does not exempt you from the need to study any number of other possible problems (for example, from the textbook.) 1. A ray of light is sent between parallel plane mirrors, as shown. The ray just misses the lower mirror as it enters the space between the two mirrors. The mirrors’ edges are aligned with one another as shown. The mirrors are 3.00 cm apart, and each is 18.0 cm long. Find the smallest initial angle of incidence so that the ray… (a) hits only the top mirror. (b) hits each mirror exactly once.

2. Standing barefoot on a level floor, at a horizontal distance of 1 m from a plane mirror mounted on a vertical wall, you can see your toes in the mirror. Your eyes are 1.50 m above the floor. (a) What is the angle of incidence of the light from your toes that reflects off the mirror into your eyes? (b) How far does the light travel from your toes to your eyes? (c) What is the greatest distance possible that the bottom of the mirror can be raised from the floor but you can still see your toes? 3. On the plane mirror system shown here, if the final angle of reflection for this ray is 14.0°, find the initial angle of incidence.

4. A spherical mirror produces an image that is located 43.0 cm behind the mirror when the object is located 12.5 cm in front of the mirror. (a) What is the focal length of the mirror? (b) Is this mirror concave or convex? 5. A 3-cm-tall object is located 8 cm in front of a concave mirror that has a 20-cm radius of curvature. Calculate the resulting image height. 6. A concave mirror has a focal length of 17.0 cm. If it is forming an image 36.0 cm in front of the mirror, what is the magnification? 7. A spherical mirror (f = 54.0 cm) produces a real image whose distance from the mirror is one-third of the object distance. (a) Find the object distance. (b) Find the image distance. 8. An object is 20.0 cm to the left of a converging lens of focal length 16.0 cm. Where must you place a second converging lens of same focal length on the right side of the first lens in order to create an image that is the same size and orientation as the object itself? 9. A concave mirror is designed so that the virtual image it produces is twice the size of the object when the object is located 19.0 cm from the mirror. What is the mirror’s radius of curvature? 10. A spherical mirror is polished on both sides. When an object is placed at a certain location so that the convex side is used as a mirror, the magnification is 1/5. What is the magnification when the mirror is reversed—so that the concave side is producing an image—assuming that the location of the object has not changed?

11. The light ray shown is traveling horizontally. In which direction will it be traveling after refracting through and exiting on the right of the darker material?

12. What is the thickness of the second-thinnest soap film (sitting on a glass plate) that will appear dark when green light (λvacuum = 567 nm) is perpendicularly incident upon it from the air above it? (nsoap = 1.35) 13. How wide is the central bright fringe that is produced by red light (λ = 660 nm) sent through a single slit (width = 1.38 μm) and projected on a wall 75.0 m away? 14. A diffraction grating has 2604 lines per centimeter, and it produces a maximum at θ = 30.0°. The grating is used with white light (containing all wavelengths between 410 and 660 nm). Which wavelength(s) could have produced this maximum? 15. A red light source, λvacuum = 660 nm, is submerged in water and pointed straight up through a submerged double slit. If the slit separation is 3.80 μm, how many fringes (if any) will emerge from the water? 16. Light is shining down into an aquarium filled with some water. The bottom of the tank is also glass. The light passes from air into water into glass and back into air. If the incidence angle at the water surface is 25O, find the angle of refraction at each interface including the last (glass-air). Use n=1.50 for glass. Sketch it. 17. A clown putting on makeup sits 27 cm from his make-up mirror. His upright, enlarged image is 65 cm from the mirror. (Which side? Positive or negative?) Find the focal length of this mirror and its magnification. 18. White light passes thru a double slit where d=0.158 mm. The diffracted light hits a screen 2.24 m away. On this screen, how far apart is the red λ = 665 nm and yellow-green λ = 565 nm 3rd order maxima? 19. A glowing light bulb is submerged 2.20 m deep in water. What’s the circle of light radius at the surface? 20. Mars, at its closest to Earth distance, is 56 million km away. If you’re talking to your astronaut buddy on Mars, what’s the time delay between you saying “hello” and hearing her respond? 21. A laser beam, in air, shines into a piece of glass of unknown index of refraction. The incident angle is 35.0O and results in some refractive angle in the glass. The glass is then lowered into a liquid of unknown refractive index. It’s seen that to get the same refractive angle in the glass, the angle of incidence must now be 20.3O. What is the refractive index of the liquid? 22. An example optical cable is made from a core of flint glass with n=1.667 and a cladding of crown glass with n=1.523. If the cable is in air (n=1.00), what is the largest possible angle A for an incident beam that will then propagate down the fiber (i.e., total internal reflection.)

23. A car at a very large distance away is imaged in a convex mirror. The car’s image is 12.0 cm from the mirror. What is the radius of curvature of the mirror? 24. You have a pair of diverging lenses, each with focal length of (negative) 8.00 cm. You align the lenses 16.0 cm apart. You place an object to the left of the first lens, 4.00 cm from the lens. Where is the resulting image of this pair of lenses?...