Exam 2 practice problems solutions

A draw a complete ray diagram for what happens to the

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a. Draw a complete ray diagram for what happens to the light from the searchlight. b. Describe mathematically the size and shape of the illuminated region at the bottom of the lake. If the illuminated region does not all appear the same color, be specific about what colors appear where. When the light from the searchlight hits the surface of lake some of the light is reflected and some is refracted. Since the refractive index of the lake water depends on wavelength dispersion will occur and the violet light will be refracted slightly more than the red light. There will be reflection at the bottom of the lake as well but it will be diffuse reflection and won’t actually look as orderly as I have it drawn in the diagram. The illuminated region at the bottom of the lake will be a circle, except that the edge of the circle will be illuminated only by red light. More colors become present as you look inward from the edge with all being present at the position you see the violet rays striking the lake bottom in the diagram. I need to determine the radii of these two circles to make this mathematically precise.
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, 1 , 1 tan tan tan sin sin tan 1 35 tan sin sin 25 15 tan 25 1.32 18.8 r r r refr r air r i water r r r r x a r D h n r D h n r m m r m For the violet light the analysis is identical except that I need to change the refractive index slightly , 1 , 1 tan tan tan sin sin tan 1 35 tan sin sin 25 15 tan 25 1.34 18.6 v v v refr v air v i water v v v r x a r D h n r D h n r m m r m 10. People who do not need glasses have lenses in their eyes that are able to clearly focus objects (meaning they look sharp and not fuzzy) that are anywhere from 20.0 cm to extremely far away from the eye (such as the stars in the night sky). a. This means that a healthy lens must be able to adjust its focal length. What range of focal lengths can it have? Hint : You will have to estimate at least 1 quantity to get a numerical answer to this. Make it reasonable. b. Someone who is nearsighted is not able to focus on distant objects. Imagine that you have a friend who is strongly nearsighted and cannot focus on anything further than 1.00 m away. In order to correct this, glasses are needed that will take the light from very distant objects and create an image just 1.00 m away. Describe the lens that will do this and determine its focal length.
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