![]() (c) Total internal reflection occurs when the incident angle is greater than the. (b) The critical angle c is the one for which the angle of refraction is. This law remains true whether the surface is rough or smooth. The ray bends away from the perpendicular. The law of reflection states that for any wave striking a surface, the angle of reflection will be equal to the angle of incidence. So the image (that is, point B) is the point (1/25, 232/25). Figure 25.4.1: (a) A ray of light crosses a boundary where the speed of light increases and the index of refraction decreases. ![]() 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. The phenomenon of total internal reflection has a wide application in optical devices such as telescopes, binoculars, periscopes, etc. These bounces will continue until the sound has. A sound wave hitting a flat wall at 45° will reflect off it at 45°. So the equation of this line is y = (-1/7)x + 65/7. What is reflection Sound waves reflect off of harder surfaces the same way billiard balls bounce off the bumpers of a pool table the angle of incidence equals the angle of reflection. Substituting the point (2,9) givesĩ = (-1/7)(2) + b which gives b = 65/7. reflection: the property of a propagated wave being thrown back from a surface (such as a mirror) refraction: Changing of a light ray’s direction when it passes through variations in matter. 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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