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MCAT Tutorial: Mirrors and Lenses

2 months ago
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2 months ago
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\({\bf{Mirrors:}}\) - lateral inversion: image is reflected across a horizontal axis (ex. the way the word AMBULANCE is mirrored on ambulances so that you see it properly in the rearview mirror) - front to back inversion: image is reflected to produce a front image and back image, ex. a plane mirror like a bathroom mirror. note that a plane mirror exhibits both types of inversion. - virtual image: the light does not originate from the image - real image: light radiates from or passes through the image - Concave & Convex Mirror: determined by the direction of curvature of the reflective surface. Mnemonic device: concave curves inward like a cave. |dw:1529505554861:dw|

2 months ago
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\({\bf{Sign~Convention~for~Mirrors:}}\) o positive for objects in front of mirror negative for objects behind mirror i positive for image in front of mirror negative for image behind mirror f center of curvature in front of mirror center of curvature behind mirror note: to determine the center of curvature, pretend the curved surface is part of a circle and draw where the "radius" would be

2 months ago
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\({\bf{Lens~Maker's~Formula:}}\) (despite its name it can work for both mirrors and lenses) 1/o + 1/i = 1/f be careful about signs

2 months ago
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\({\bf{Drawing~Ray~Diagrams}}\) to locate the position and orientation of an image Concave Mirror (converging) 1. draw the object in the correct position and orientation, if not already given 2. draw a straight horizontal line from the top of image, reflect off the mirror, and through the focal point. 3. draw another line from the top of the image, this time go through the focal point and bounce off the mirror horizontally 4. the point where the two rays intersect will be the new top of the image. extend the rays as needed if they do not intersect. Convex Mirror (diverging) 1. draw the object in the correct position and orientation, if not already given 2. draw a straight horizontal line from the object to the mirror. however, this time the ray bounces off in a direction opposite but parallel to the focal point (see the diagram). draw a dashed line to indicate that the ray does not cross through the focal point, but in a direction away from it. (see diagram) 3. draw a ray from the top of the object, in the direction of the focal point, but again, the ray does not cross the mirror but instead bounces off in the horizontal direction. continue the horizontal line through the mirror, except dashed this time, to show that the ray does not cross the mirror. 4. the intersection of the two dashed lines is where the top of the image forms.

2 months ago
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\({\bf{Sign~Convention~for~Lenses}}\) o positive for objects in front of lens negative for objects behind a lens i positive for image on the opposite side of the lens as the object (this is diff. than the rule for mirrors so be careful) negative for image on the same side of the lens as the object f center of converging lens (concave) center of diverging lens (convex) note that this designation of converging/concave, etc. is the opposite for mirrors

2 months ago
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\({\bf{Drawing~Ray~Diagrams}}\) for lenses convex lens (converging) 1. start from the top of the object, draw a horizontal line to the lens, then reflect through the lens and converge at the focal point 2. start from the top of the object, draw a line through the focal point, then hit the center of the lens and reflect horizontally 3. the point where the rays converge is the image location |dw:1529508327334:dw| concave lens (diverging) 1. start from the top of the object, draw a horizontal line to the lens, then diverge in the opposite direction as the focal point. then draw a dashed line from the reflection point through the focal point to indicate that the ray does not cross through the focal point 2. start from the top of the object, draw a line through the center of the lens, 3. the point of intersection is the new location of the image. |dw:1529508520027:dw|

2 months ago
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More about the sign convention of mirrors, lenses, and their images |dw:1529508619461:dw| |dw:1529508631544:dw|

2 months ago
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Anyway, that's the end of my tutorial, I hope it was a helpful resource. Source material is the 2nd Edition Barron's Prep book for the new MCAT

2 months ago
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