f5ch35 - 956 CHAPTER 35 GEOMETRICAL OPTICS CHAPTER 35...

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956 CHAPTER 35 GEOMETRICAL OPTICS C HAPTER 35 Answer to Checkpoint Questions answer to kaleidoscope question: two mirrors that form a V with an angle of . : d , : d : d . ( a ) real; ( b ) inverted; ( c ) same . ( a ) e ; ( b ) virtual, same . virtual, same as object, diverging Answer to Questions . c . c . ( a ) a ; ( b ) c . ( a ) x axis; ( b ) no, no; ( c ) direction in which your nose points . ( a ) no; ( b ) yes (fourth is o mirror end) . ( a ) a and c ; ( b ) three times; ( c ) you . ( a ) from in nity to the focal point; ( b ) decrease continually . convex . ( d ) (in nite), tie of ( a ) and ( b ), then ( c ) . ( a ) decrease; ( b ) increase; ( c ) increase . mirror, equal; lens, greater . ( a ) : : : ; ( b : , plus; : , ; : , minus . ( a ) all but variation ; ( b ) for , , and : right, inverted; for and : left, same . ( a ) and ( b ) rightward
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image hummingbird camera d 1 d d 3 d 2 d 2 d 2 CHAPTER 35 GEOMETRICAL OPTICS 957 . ( a ) less; ( b ) less Solutions to Exercises & Problems E ( a ) Virtual, since the image is formed by plane mirrors. ( b ) Same. In fact you can easily verify this by locating, for example, the images of two points, one at the head of the penguin and the other at its feet. ( c ) Same, since the image formed by any plane mirror retains the original shape and size of an object. ( d ) The image of the penguin formed by the top mirror is located a distance D above the top mirror, or L + D above the bottom one. Thus the nal image of the penguin, formed by the bottom mirror, is a distance L + D from the bottom mirror. E ( a ) Let the separation between you and the mirror be s , then the separation between you and your image is s . So your image moves toward you at a speed v i = d ( s ) =dt = ds=dt = v: ( b ) Since the separation between the image and the mirror is also s , the image also moves toward the mirror at speed v . E The image is cm behind the mirror and you are cm in front of the mirror. You must focus your eyes for a distance of cm + cm = cm. E Refer to the diagram to the right. The focus distance is d = q ( d + d ) + d = p ( : m + : m) + ( : m) : m :
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α φ θ A' A B O O' object I 1 I 2 object I 2 I 3 958 CHAPTER 35 GEOMETRICAL OPTICS E Consider A , the image of A in the mirror. The actual path of light from A to B is AOB , for which the angle of incidence satis es + = and the angle of re ection satis es + : So = . To show that any other path, such as AO B as shown, is longer than AOB , just note in the gure that AO + O B = A O + O B > A B = A O + OB = AO + OB : E ( a ) There are three images. Two are formed by single re ections from each of the mirrors and the third is formed by successive re ections from both mirrors. ( b ) The positions of the images are shown on the two diagrams below. The diagram on the left shows the image I , formed by re ections from the left-hand mirror. It is the same distance behind the mirror as the object O is in front and is on the line that is perpendicular to the mirror and through the object. Image I is formed by light that is re ected from both mirrors. You may consider I to be the image of I formed by the right-hand mirror, extended. I is the same distance behind the line of the right-hand mirror as I is in front and it is on the line that is perpendicular to the line of the mirror.
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f5ch35 - 956 CHAPTER 35 GEOMETRICAL OPTICS CHAPTER 35...

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