Physics for Scientists and Engineers Electrodynamics, Optics, and Special Relativity
Physics for Scientists and Engineers Electrodynamics, Optics, and Special Relativity PHYSICS 1C
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This 2 page Class Notes was uploaded by Arvilla Bernhard on Friday September 4, 2015. The Class Notes belongs to PHYSICS 1C at University of California - Los Angeles taught by Staff in Fall. Since its upload, it has received 72 views. For similar materials see /class/177937/physics-1c-university-of-california-los-angeles in Physics 2 at University of California - Los Angeles.
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Date Created: 09/04/15
Physics 1C Conventions for Mirror Equations and Lens Equations Depending on your own tastes and brain structure one of these sets of conventions may be more appealing to you Use whichever one you prefer Giancoli s Traditional Conventions o Giancoli uses the same equations for mirrors and lenses 1 1 hi d1 f 7 hide m if 1 do but different conventions in each case for the signs of quantities A 1 represents a distance that may be positive or negative 010 is the distance from the mirrorlens to the object di is the distance from the mirrorlens to the image 1 represents a distance called the focal length which can be positive or negative f is the distance from the mirrorlens to the focal point ho the height of the object is taken to be positive in all cases and hi the height of the image is positive for an upright image and negative for an inverted image relative to the object m is the lateral magni cation of the image Due to the convention for hi it is positive for an upright image and negative for an inverted image relative to the object Parabolic Mirror Equations Conventions When the object image or focal point is on the side of the mirror from which the light is coming on the re ecting side the corresponding distance is considered positive If any of these points is behind the mirror the corresponding distance is negative So the focal length is positive for concave mirrors and negative for convex mirrors 0 Thin Lens Equations Conventions The focal length is positive for converging lenses and negative for diverging lenses Different conventions for object and image The object distance is positive if it is on the side of the lens from which the light is coming this is usually the case although when lenses are used in combination it might not be so otherwise it is negative The image distance is positive if it is on the opposite side of the lens from where the light is coming if it is on the same side di is negative Equivalently the image distance is positive for a real image and negative for a virtual image Alternate Consistent Conventions c We may use different equations for mirrors and lenses but the same conventions in each case The lateral magni cation is the same for each 7 241 961 m 7 77 yo 0 7 The focal length 1 is a positive quantity always just as anything called length should be Anything called a distance should also be positive We will thus refer to relative positions instead which can be negative 7 De ne an m axis along the principle axis of the mirror or lens and a y axis perpendicular to it Let the position of the mirror or lens be m 0 and the position of the m axis be y 0 It doesn t matter which way either of the axes points M is the position of the focal point that is relevant for incoming rays that are parallel to the axis A mirror has only one focal point but lenses have two one of which is relevant for these parallel rays 0 is the position of the object mi is the position of the image These m positions or axial positions are relative to the mirror or lens which is at z 0 and their signs are immediately apparent in a ray diagram once the m axis is de ned Note that either zf 1 or M 7f yo is the lateral position of a point on the object usually the extremal lateral point which would give the height using Giancoli s conventions if one side of the object is on the axis yi is the lateral position of the point in the image corresponding to the point on the object chosen for yo These y positions or lateral positions are relative to the axis which is at y 0 and their signs are immediately apparent in a ray diagram once the y axis is de ned 0 Parabolic Mirror Equation1 0 Thin Lens Equation and Convention 221 zf 270 7 For lenses there are two focal points each of which are equally relevant in a ray diagram As stated above by convention we choose to use the focal point that is relevant for incoming rays that are parallel to the axis for converging lenses the focal point on the side to which the light is going for diverging lenses the focal point on the side from which the light is coming 1The equation is organized so that the quantities you would naively expect to know are on the right so you can plug in known values and nd the unknown quantity on the left Of course in a given problem the knowns and unknowns can be di erent
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