PROBLEMS
1. In 2011 a research group from Korea, M Choi, et al, produced a material with a record-breaking refractive index of 38.6. What is the speed of light in that metamaterial?
2. What is the angle of the cone of light in Snell's window?
3. From an under-water vantage point while looking through Snell's window, at what angle with respect to vertical would you have to look in order to see the sun when it is 45 degrees above the horizon?
4. What do you see in the diving scenario when looking at the water/air interface at an angle of 60 degrees with respect to vertical?
5. Can material particles exceed the speed of light? Explain.
6. Visible light falls in the range of approximately 400nm to 700nm. What are the associated wavelengths in water? What are the associated frequencies in ethanol?
7. What color should we expect at the top of a primary rainbow? Bottom?
8. Why is a secondary rainbow much dimmer than a primary rainbow?
9. The angle between sunlight and a person's line of sight when viewing a primary rainbow is approximately . What would change that value?
10. Unpolarized light is passed through a polarizer. What intensity results?
11. Another polarizer is added after the one in the problem above. The second one has a transmission axis aligned at an angle of with respect to the first one. What intensity in terms of the initial, unpolarized intensity results?
12. A third polarizer is added after those two at with respect to the first polarizer. What intensity comes out of the third polarizer?
13. You wish to take a photograph of a road at dusk, and want to see car tail lights as very long red lines. Since the sun is just setting, your camera is only keeping the shutter open for 0.5s. You estimate that with a 10s shutter time you will achieve your desired effect. How will you orient two polarizers to make this possible?
14. What angle is required between two polarizers to reduce the intensity of sunlight to 5% of its value? Careful about just plugging in mindlessly!
15. An object is placed 30cm away from a lens of focal length 20cm. What type of image is formed? Where is it? Is it upright or inverted? Please do this both by ray tracing and by algebraic means.
16. At what distance must an object be placed from a converging lens of focal length f in order to form an image of magnification -1?
17. A myopic patient has a far point of 30cm. What is the appropriate lens to prescribe in diopters?
18. A hyperopic individual has a near point of 0.80m. What lens should be prescribed in diopters?
19. In a hyperopic eye, does the image form before or after the retinal surface when holding an object at a healthy eye's near point?
20. Derive the law of reflection using Fermat's principle of least time.
21. Derive the law of refraction (Snell's law) using Fermat's principle of least time.
ANSWERS
1. 7.77x106m/s
2. 48.8o half angle of the cone
3. 32.0o
4. bottom of pool or lake... perhaps darkness.
5. yes in media besides vacuum
6. 300-526nm; 7.5x1014Hz and 4.3x1014Hz
7. see pictures and chapter description
8. Because it's a double reflection... intensity is lost.
9. Shape of drops or refractive index of water changing.
10. 50%
11. 3/8Io
12. 35% if rotated in same direction as first polarizer
13. 71.6o
14. 71.6o
15. real; 60cm; inverted
16. do=2f
17. -3.33m-1
18. 2.75m-1
19. after
20. see notes
21. see notes