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Unformatted text preview: Physics 1112 Spring 2008 PS #2 Solutions Page 1 of 8 Physics 1112 Problem Set #2 Solutions Problem 1: Two non-parallel light rays initially converge to a single point on a screen. A rectangular block of glass is now placed somewhere in front of the screen, in the path of the light rays, so that the glass surface is parallel to the screen. Where is the new convergence point of the rays? The rays will no longer converge on the screen. Instead, the convergence point will away from the glass slab , as shown by the diagram. After leaving the glass, the rays are traveling in the same direction as they were before (because the glass is a slab with parallel faces). However, the rays have been displaced a bit. It’s this displacement that causes the convergence point to move. Problem 2: While standing on a lakeside pier, you see a fish in the water and decide to try some less common methods of snagging dinner. (a) If you try to snag the fish with a harpoon, where should you aim? (b) Where should you aim if you instead use a high-powered laser to zap the fish? (a) To answer this question, you need to understand that the fish is not actually where you see it, due to refrac- tion. Light rays coming from the fish bend away from the normal as they travel from water into air. As a re- sult, you perceive the fish to be above where it actually is. Your harpoon won’t change direction when it enters the water, so in order to hit the actual fish, you should aim below where you see the image of the fish. (b) Using the laser, you should aim directly at (the image of) the fish. Unlike an arrow, laser light will be refracted by the water. If you aim in the direction where you see the fish, the laser light will refract by exactly the same amount as the light coming from the fish to your eyes (just in reverse). Physics 1112 Spring 2008 PS #2 Solutions Page 2 of 8 Problem 3: Two blocks made from the same transparent material are immersed in two different liquids. A ray of light strikes each block at the same angle of incidence, as shown in the figure. Which liquid has the greater index of refraction? Liquid B Liquid A To start with, it’s important to realize that the block material has a higher index of refraction than either liquid. We can see this from the diagram: in both cases, light bends toward the normal as it goes from liquid to block. Next, note that for the block in liquid A, the light bends more sharply as it enters the block, compared with liquid B. That implies that the index of refraction for liquid B is closer to the refraction index of the block than the index for liquid A is. (From Snell’s Law, n 1 sin θ 1 = n 2 sin θ 2 , you can see that the closer in value n 1 is to n 2 , the closer θ 1 and θ 2 have to be.) Putting these two observations together tells us that n A < n B < n block , so liquid B has the greater index of refraction....
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- Spring '08
- Light, Snell's Law, Sin, Total internal reflection, rays