Lecture_23 - 25.6 Mirror and Magnification Equations Lets...

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25.6 Mirror and Magnification Equations Let’s define the following quantities: f = the focal length of the mirror d o = the object distance from mirror d i = the image distance from mirror m = the mirror magnification h o = the object height h i = the image height We can use a little geometry and properties of similar triangles to show that the following relationships are true: f d d i o 1 1 1 = + The mirror equation o i o i d d h h m - = = = height Object height Image The magnification equation
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These two equations provide a complete description of the images formed by mirrors: (1) The location of the object and image, (2) The size of the object and image, and (3) Whether the object is upright or inverted. From the magnification equation, we see that: If m > 1 , the image is enlarged . If m < 1 , the image is reduced . If m is positive , the image is upright with respect to the object. If m is negative , the image is inverted with respect to the object.
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Sign Conventions Focal Length f is positive for concave mirrors f is negative for convex mirrors Object Distance d o is positive if the object is in front of the mirror d o is negative if the object is behind the mirror Image Distance d i is positive if the image is in front of the mirror (real image) d i is negative if the image is behind the mirror (virtual image)
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