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hw5 - CHAPTER 36 IMAGE FORMATION A ND OPTICAL INSTRUMENTS F...

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CHAPTER 36 IMAGE FORMATION AND OPTICAL INSTRUMENTS ActivPhysics can help with these problems: All activities in Section 15 Sections 36-1 and 36-2: Plane and Curved Mirrors Problem 1. A shoe store uses small floor-level [email protected] let customers view prospective purchases. At what angle should such a mirror be inclined so that a person standing 50 cm from the mirror with eyes 140 cm off the floor can see her feet? Solution A small mirror (M) on the floor intercepts rays coming from a customer's shoes (O), which are traveling nearly parallel to the floor. The angle to the customer's eye (E) from the mirror is twice the angle of reflection, so tan 2a = h/d, or a = tan-' x (140150) = 35.2", for the given distances. Therefore, the plane of the mirror should be tilted by 35.2" from the vertical to provide the customer with a floor-level view of her shoes. Problem 1 Solution. Problem 2. Two plane mirrors occupy the first four meters of the positive a and y-axes, as shown in Fig. 36-44. Find the locations of all images of an object at z = 2 m , y = l m . FIGURE 36-44 Problem 2 Solution. Solution In addition ,to the two direct images in each mirror (one reflection) at I, = (-2 m, 1 m) and I, = (2 m, -1 m), a multiple image (two reflections) also appears at I,, = (-2 m, -1 m). (The latter is the image in one mirror of the direct image in the other.) Ray tracing confirms this, as shown on Fig. 36-44. No more than two reflections are possible for perpendicular mirror planes, so these are all the images. Problem 3. (a) What is the focal length of a concave mirror if an object placed 50 cm in front of the mirror has a real image 75 cm from the mirror? (b) Where and what type will the image be if the object is moved to a point 20 cm from the mirror? Solution (a) The mirror equation relates the given distances (both positive for a real object and image) to the focal length: f-' = (50 cm)-I + (75 cm)-l, or f = 30 cm.

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