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CH35 - PART 5 OPTICS CHAPTER 35 REFLECTION AND REFRACTION...

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PART 5—OPTICS CHAPTER 35—REFLECTION AND REFRACTION ActivPhysics can help with these problems: Activities 15.1, 15.2 Section 35-2:—Reflection Problem 1. Through what angle should you rotate a mirror in order that a reflected ray rotate through 30 ° ? Solution Since θ θ 1 1 = for specular reflection, (Equation 35-1) a reflected ray is deviated by φ θ = ° - 180 2 1 from the incident direction. If rotating the mirror changes θ 1 by θ 1 , then the reflected ray is deviated by φ θ = - 2 1 or twice this amount. Thus, if φ θ = ° = ° 30 15 1 , . Problem 1 Solution. Problem 2. The mirrors in Fig. 35-33 make a 60 ° angle. A light ray enters parallel to the symmetry axis, as shown. (a) How many reflections does it make? (b) Where and in what direction does it exit the mirror system? Solution The first reflected ray leaves the upper mirror at a grazing angle of 30 ° , and therefore strikes the lower mirror normally. It is then reflected twice more in retracing its path in the opposite direction. FIGURE 35-33 Problem 2 Solution. Problem 3. To what angular accuracy must two ostensibly perpendicular mirrors be aligned in order that an incident ray returns on a path within 1 ° of its incident direction? Solution A ray incident on the first mirror at a grazing angle α is deflected through an angle 2 α (this follows from the law of
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CHAPTER 35 reflection). It strikes the second mirror at a grazing angle β , and is deflected by an additional angle 2 β . The total deflection is 2 2 2 180 α β θ + = ° - ( ). If this is to be within 180 1 ° ± ° , then the angle between the mirrors, θ , must be within 90 1 2 ° ± ° . Problem 3 Solution. Problem 4. If a light ray enters the mirror system of Fig. 35-33 propagating in the plane of the page and parallel to one mirror, through what angle will it be turned? Solution Entering parallel to the top mirror, a ray makes an angle of incidence of 30 ° with the bottom mirror. It then strikes the top mirror also at 30 ° incidence, and is reflected out of the system parallel to the bottom mirror (see the completion of Fig. 35-33). The total deflection is 240 ° CCW (or 120 ° CW) from the incident direction. FIGURE 35-33 Problem 4 Solution. Problem 5. Suppose the angle in Fig. 35-33 is changed to 75 ° . A ray enters the mirror system parallel to the axis. (a) How many reflections does it make? (b) Through what angle is it turned when it exits the system? Solution Now, after the first reflection, the ray leaves the top mirror at a grazing angle of 37 1 2 ° , and so makes a grazing angle of 180 75 37 67 1 2 1 2 ° - ° - ° = ° with the bottom mirror. It is therefore deflected through an angle of 2 37 2 67 1 2 1 2 ( ) ( ) ° + ° = 210 ° CW, as it exits the system, after being reflected once from each mirror. 56
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CHAPTER 1 L FIGURE 35-33 Problem 5 Solution. Problem 6. Two plane mirrors make an angle φ .
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