Homework 3 Solution

Homework 3 Solution - Version PREVIEW Homework 3 Savrasov...

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Unformatted text preview: Version PREVIEW Homework 3 Savrasov (39825) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Air to Diamond 001 10.0 points Light is incident at an angle of 40 on the surface of a diamond. Find the angle of refraction. Correct answer: 15 . 4035 . Explanation: By Snells Law, for an angle of incidence and an angle of refraction , n air sin = n sin sin = sin n , since n air = 1. = arcsin parenleftbigg sin n parenrightbigg . Drinking Glass Bottom 04 002 10.0 points An cylindrical opaque drinking glass has a diameter 6 cm and height h , as shown in the figure. An observers eye is placed as shown (the observer is just barely looking over the rim of the glass). When empty, the observer can just barely see the edge of the bottom of the glass. When filled (with a transparent liquid with an index of refraction of 1 . 26) to the brim, the observer can just barely see the center of the bottom of the glass. i h 6 cm r e y e Calculate the angle r . Correct answer: 63 . 7321 degrees. Explanation: Looking at the figure below, R r R i i h r d r e y e After filling the glass with liquid, we know from Snells law that n liquid sin i = n air sin r . The radius r is one-half the diameter d , there- fore sin i r R i = r r 2 + h 2 . Now we can solve for h . Substituting our expressions for the sines into Snells Law, we get n liquid r r 2 + h 2 = n air d d 2 + h 2 , so n 2 liquid r 2 ( d 2 + h 2 ) = n 2 air d 2 ( r 2 + h 2 ) . We can simplify this by using n air = 1 . 0, n liquid = n , and d = 2 r h 2 ( d 2- n 2 r 2 ) = d 2 r 2 ( n 2- 1) h 2 bracketleftbig (2 r ) 2- n 2 r 2 bracketrightbig = d 2 r 2 ( n 2- 1) h 2 r 2 (4- n 2 ) = d 2 r 2 ( n 2- 1) h 2 (4- n 2 ) = d 2 ( n 2- 1) , so d h = radicalBigg (2 r ) 2- n 2 r 2 r 2 ( n 2- 1) = radicalBigg 4- n 2 n 2- 1 . Version PREVIEW Homework 3 Savrasov (39825) 2 we see from the geometry that tan r d h , therefore r = arctan parenleftbigg d h parenrightbigg = arctan radicalBigg 4- n 2 n 2- 1 = arctan radicalBigg 4- (1 . 26) 2 (1 . 26) 2- 1 = 63 . 7321 ....
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Homework 3 Solution - Version PREVIEW Homework 3 Savrasov...

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