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1 page/≈550 words
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MLA
Subject:
Technology
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Term Paper
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English (U.K.)
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Topic:

Snell's Law Project (Term Paper Sample)

Instructions:
The task was to investigate the Snell\'s Law and verify it mathematically. This was a physics term paper. source..
Content:
Name Instructor Course Date Snell's Law Project Snell's Law is also called the Law of Refraction. It explains the relationship between the angles of refraction and incidence for a wave hitting on an interface between 2 media with different refraction indices. The objective of the project was to verify Snell's Law using a mathematical model. left188788 In this case, n1 & n2 are the refractive indices of media 1& 2 in that order. While θ1 & θ2 represent incident & refracted angles respctively. (#1) Assume we have a light source at the point A (-1,3) and the x-axis is a mirrored surface. A ray of light travels from A toward the origin and ends up at B (1, √3). For a perfect mirror, i=r. In the above diagram, i=r=30⁰ Tan (30⁰) = oppadj= 1√3 (#2) Optimization Assume the light source is at A (0, 2). If the ray bounces off the x-axis and end up at B (4, 1) Let x be the coordinate on the x-axis Since I =R, we can find the total distance Travelled by the light wave. Let X be the point at which the incident Ray hits the x-axis before bouncing off. OX = √x2 + 22 BX = √(4-x)2 + 12 * The total distance is a function of x (0≤x≥4) fx= √x2 + 22 + √(4-x)2 + 12 = √x2 + 4 + √x2 - 8x + 17 f' (x)=x√(x2-4) + x-4√(x2-8x+17 = 0…………………………….. (i) Rearranging the equation (i) we get. x√(x2-4) = x-4√(x2-8x+17 Cross-multiplying the equation and squaring both sides to eliminate the root sign, we get x2(x2-8x+17)-(4-x)2(x2-4) x4- 8x3+ 17x2=(16-8x+x2) (x2-4) = 16x2−64 − 8x3 − 32x+ 4x4 17x2= 20x2 − 32x + 64 3x2 − 32x + 64 = 0…………………………… (ii) This is a quadratic equation which can be solved using the quadratic formula, x=-b±b2-4ac2a, where a=3, b=-32, c= 64 Substituting for a, b, & c in the above equation, we obtain x1,2 = 32 ± 166 = x1 =8 & x2 = 83 x=83 * 369697020447000-335009430543500 180892323116800-255460550355500 ...
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