handout_11_06

# handout_11_06 - ratio of the sine of the angle of incidence...

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MATH 1A: OPTIMIZATION (PART II) 1. The Statue of Liberty is 32 m tall, and rests on a base 49 m tall. How far away from the base should you stand to get the best view of the statue? (In other words, to maximize the angle subtended by the statue at your eye.) 2. Consider the ellipse x 2 + 4 y 2 = 4. Find the point on the ellipse furthest from (0 , 2). Date : November 6, 2009. 1

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3. In optics, “Fermat’s principle of least time” says that the path taken between any two points by a ray of light is the path that can be traversed in least time. 1 . We will use this to derive two famous laws in optics. (1) Consider light reﬂecting oﬀ a (straight) mirror, as shown. Show that the angle of incidence i is equal to the angle of reﬂection r . (2) Light has diﬀerent speed in diﬀerent media. Consider a ray of light entering water. Show that the
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Unformatted text preview: ratio of the sine of the angle of incidence to the angle of refraction is equal to the ratio of the speeds of light in air and that in water. 4. The cost (in dollars) of producing n cars of a certain model is 10000 n + 15000 n + 1 , The cars are sold for \$12 , 000 each. Based on this information, how many cars should be produced to maximize proﬁt? Do you think this answer is sensible? 5. Let b x c denote the greatest integer which is less than or equal to x . In other words, b x c is x rounded down to an integer. Find the point on the graph of y = b x c + x which is closest to the point (1 , 0). What about the point (2 , 0)? 1 Wikipedia:Fermat’s principle 2...
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## This note was uploaded on 03/27/2012 for the course MATH 1a taught by Professor Benedictgross during the Fall '09 term at Harvard.

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handout_11_06 - ratio of the sine of the angle of incidence...

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