Assess ray tracing will confirm these results 2337

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Assess: Ray tracing will confirm these results.

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23.37. Solve: The image is at 40 cm as seen in the figure. It is inverted. Assess: When the object is outside the focal length we get an inverted image.
23.38. Solve: The image is at 30 cm as seen in the figure. It is upright. Assess: When the object is within the focal length we get a magnified upright image.

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23.39. Solve: The image is at 12 cm as seen in the figure. It is upright. Assess: We expected an upright virtual image from the convex mirror.
23.40. Model: The speed of light in a material is determined by the refractive index as . v c n = Solve: To acquire data from memory, a total time of only 2.0 ns is allowed. This time includes 0.5 ns that the memory unit takes to process a request. Thus, the travel time for an infrared light pulse from the central processing unit to the memory unit and back is 1.5 ns. Let d be the distance between the central processing unit and the memory unit. The refractive index of silicon for infrared light is n Si = 3.5. Then, ( ) ( )( ) ( ) 9 8 Si Si Si Si 1.5 10 s 3.0 10 m/s 1.5 ns 2 2 2 1.5 ns 2 2 3.5 c d d dn d v c n c n × × = = = = = d = 6.4 cm

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23.41. Model: Treat the red ball as a point source and use the ray model of light. Solve: (a) Using the law of reflection, we can obtain 3 images of the red ball. (b) The images of the ball are located at B, C, and D. Relative to the intersection point of the two mirrors, the coordinates of B, C, and D are: B( + 1 m, 2 m), C( 1 m, + 2 m), and D( + 1 m, + 2 m). (c)
23.42. Model: Treat the laser beam as a ray and use the ray model of light. Visualize: Solve: From the geometry of the mirrors and the rays, 50 , =30 , and 20 . β α φ = ° ° = °

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23.43. Model: For a mirror, the image distance behind the mirror equals the object’s distance in front of the mirror. Visualize: Solve: Your face is 2.0 from the mirror into which you are looking. The image of your face (image 1) is 2.0 m behind the mirror, or 4.0 m away. Behind you, the image of the back of your head (image 2) is 3.0 m behind the mirror on the other wall. You can’t see this image because you’re looking to the right. However, the reflected rays that appear to come from image 2 (a virtual image) act just like the rays from an object—that is, just as the rays would if the back of your head were really at the position of image 2. These rays reflect from the mirror 2.0 m in front of you into which you’re staring and form an image (image 3) 8.0 m behind the mirror. This is the image of the back of your head that you see in the mirror in front of you. Since you’re 2.0 m from the mirror, the image of the back of your head is 10 m away.
23.44. Model: Treat the laser beam as a ray and use the ray model of light. Visualize: As the cylinder rotates by an angle θ , the path of the reflected laser beam changes by an angle 2 θ relative to the direction of incidence.

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