Sign In
Not register? Register Now!
Essay Available:
You are here: HomeTerm PaperTechnology
1 page/≈550 words
Term Paper
English (U.K.)
MS Word
Total cost:
$ 12.96

Snell's Law Project (Term Paper Sample)

The task was to investigate the Snell\'s Law and verify it mathematically. This was a physics term paper. source..
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 ...
Get the Whole Paper!
Not exactly what you need?
Do you need a custom essay? Order right now:

Other Topics:

  • Technology's social side effect
    Description: Technology's social side effect Technology Term Paper...
    3 pages/≈825 words| MLA | Technology | Term Paper |
  • Major Universities in Australia
    Description: This paper provides an analysis of websites of three major universities in Australia: The University of Sydney, The University of Queensland and Monash University....
    5 pages/≈1375 words| MLA | Technology | Term Paper |
  • Security Testing in Mobile Application and Web Application
    Description: The objective of this project is to focus on the security threats experienced in web and phone application....
    10 pages/≈2750 words| 8 Sources | MLA | Technology | Term Paper |
Need a Custom Essay Written?
First time 15% Discount!