The normal line at the point of incidence is different for different rays. However, the roughness of the material means that each individual ray meets a surface which has a different orientation. Why Does a Rough Surface Diffuse A Beam of Light?įor each type of reflection, each individual ray follows the law of reflection. On the other hand, if the surface is microscopically rough, the light rays will reflect and diffuse in many different directions. If the bundle of light rays is incident upon a smooth surface, then the light rays reflect and remain concentrated in a bundle upon leaving the surface. Each individual light ray of the bundle follows the law of reflection. The diagram below depicts two beams of light incident upon a rough and a smooth surface.Ī light beam can be thought of as a bundle of individual light rays which are traveling parallel to each other. Whether the surface is microscopically rough or smooth has a tremendous impact upon the subsequent reflection of a beam of light. Reflection off of rough surfaces such as clothing, paper, and the asphalt roadway leads to a type of reflection known as diffuse reflection. Reflection off of smooth surfaces such as mirrors or a calm body of water leads to a type of reflection known as specular reflection. The picture at the right depicts a highly magnified, microscopic view of the surface of a sheet of paper. Your clothing, the walls of most rooms, most flooring, skin, and even paper are all rough when viewed at the microscopic level. Most objects which reflect light are not smooth at the microscopic level. But quite obviously, mirrors are not the only types of objects which light reflects off of. As such, they offer each individual ray of light the same surface orientation. Mirrors are typically smooth surfaces, even at the microscopic levels. In physics class, the behavior of light is often studied by observing its reflection off of plane (flat) mirrors. (regardless of the orientation of the surface) Each ray strikes a surface with a different orientation yet each ray reflects in accordance with the law of reflection. A series of incident rays and their corresponding reflected rays are depicted in the diagram below. As long as the normal (perpendicular line to the surface) can be drawn at the point of incidence, the angle of incidence can be measured and the direction of the reflected ray can be determined. This predictability concerning the reflection of light is applicable to the reflection of light off of level (horizontal) surfaces, vertical surfaces, angled surfaces, and even curved surfaces. The light ray will then reflect in such a manner that the angle of incidence is equal to the angle of reflection. Once a normal to the surface at the point of incidence is drawn, the angle of incidence can then be determined. So the image (that is, point B) is the point (1/25, 232/25).It was mentioned earlier in this lesson that light reflects off surfaces in a very predictable manner - in accordance with the law of reflection. So the intersection of the two lines is the point C(51/50, 457/50). Now we need to find the intersection of the lines y = 7x + 2 and y = (-1/7)x + 65/7 by solving this system of equations. So the equation of this line is y = (-1/7)x + 65/7. So the desired line has an equation of the form y = (-1/7)x + b. Since the line y = 7x + 2 has slope 7, the desired line (that is, line AB) has slope -1/7 as well as passing through (2,9). So we first find the equation of the line through (2,9) that is perpendicular to the line y = 7x + 2. Then, using the fact that C is the midpoint of segment AB, we can finally determine point B.Įxample: suppose we want to reflect the point A(2,9) about the line k with equation y = 7x + 2. Then we can algebraically find point C, which is the intersection of these two lines. So we can first find the equation of the line through point A that is perpendicular to line k. Note that line AB must be perpendicular to line k, and C must be the midpoint of segment AB (from the definition of a reflection). Let A be the point to be reflected, let k be the line about which the point is reflected, let B represent the desired point (image), and let C represent the intersection of line k and line AB.
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