AMS 261 Optional Project: Reflecting Light Jacob Crosser June 2022 1 Introduction The purpose of this project is to study the reflection of photons of light off of surface. Specifically, you will be examining the "Law of Reflection," which in the context of mirror-like surfaces produces a phenomenon known as specular reflection. In short, the Law of Reflection says that when light is reflected off of a surface the angle of reflection relative to the normal vector of the surface (at the point of contact) is the same as the angle of incidence with relative to that same normal vector. This is shown in Figure , where it is illustrated that 01 = 02. We are going to leverage our understanding of multivariate calculus to study how different surfaces reflect light. 2 Necessary Coding Skills . Creating/evaluating functions . Plotting surfaces . Plotting vector fields 3 Required Materials To receive full credit for this project, you will have to submit the following materials: 1. A write up of the project. Expectations for this are given below. 2. All code you wrote for this project. I should be able to run your code and get your results and figures. This can just be attached to the end of your write up or as separate file.n' 0 2 T Figure 1: (Law of Reflection) The angle of reflection 02 of a light ray is the same as the angle of incidence 02, both relative to the surface normal vector. 4 The Project 1. Let the vector v represent the intensity of a ray of photons moving in a specific direction (i.e. v| is the intensity, and v is the direction). The vector is three-dimensional. Using the Law of Reflection, begin the project by finding the finding the vector describing the reflected light Vr in terms of the incoming light vector v; and the normal vector of the surface n. Assume that the intensity of the reflected light is the same as the intensity of the incoming light (note: this is a simplification of the real, physical system). Include your derivation of the vector Vr, as well as a (one or two sentence) written explanation giving intuition about your formula. 2. Consider the plane given by r - 2y + z = 0. We're going to look at the way a beam of light is reflected off of it. a) Plot the plane for the region for -5