OPTI 201R 10 L8 - OPTI 201R Fall 2010 8-1 Ch. 4 Mirrors and...

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Unformatted text preview: OPTI 201R Fall 2010 8-1 Ch. 4 Mirrors and Prisms 4.1 Plane Mirrors "A plane mirror not only bends or changes the path of reflected light rays; it also changes the handedness (parity) of a reflected image." ! bends please reserve this word for refraction " changes the handedness (parity) (yes!) Handedness = (-1) m (4.1) ! "A result of +1 yields right-handedness (even parity), while a result of -1 yields left-handedness (odd parity)." (this statement only true if the object has even parity, i.e. is "right-handed") " "A result of +1 indicates no change in the handedness (parity), while a result of -1 indicates a change in the handedness (parity)." Figure 4.1 NOTE: When choosing a letter as a "test" object, pick one that doesn't have vertical or horizontal symmetry: Good choices: F R P J etc. Bad choices: X H I M O U etc. OPTI 201R Fall 2010 8-2 Figure 4.3 Plane mirror forming the virtual image of "R" to the observer. 4 points to note about a single reflecting surface : (1) A line connecting the object and its image is perpendicular to the mirror surface and is bisected by the mirror. (2) The image handedness is changed. (yes! " ) (3) Any point on the mirror plane is equally distant from the object and its image. (4) The angles of reflection follow Snell's Law. Figure 8.2 Projection of a line object through a plane mirror. OPTI 201R Fall 2010 8-3 "Cascaded" Plane Mirrors Parallel to each other: # The mirrors are parallel to each other, separated by a distance d. # The image is displaced from the object by a distance = 2d. # The object and image lie on a line that is perpendicular to the plane of the mirror(s). # The image is virtual and has no change in parity (2 reflections). # The output rays appear to diverge from the image point. # Each output ray is parallel to the corresponding input ray. # This is a periscope! OPTI 201R Fall 2010 8-4 At an angle ! < 90 to each other: !"#$%& ()* +,- ./01& 2"%%-%3 ./04&5 06 01 01#/& 7 forming a dihedral edge. # The intersection of the two mirror surfaces forms a line called the dihedral line (or dihedral edge ). # A plane perpendicular to the dihedral edge is called a principal projection . # The angle between the two mirrors 8 78 is called the dihedral angle . # A ray in the principal projection plane is deviated by twice the angle between the mirrors (i.e. by twice the dihedral angle). 9 : ;7 (4.2) # +<& 5&="06"-1 01#/& 9 "3 "15&.&15&16 -> 6<& "1.$6 01#/&8 A, >-% 7 ? 90. # @<&1 7 < 90 the rays cross each other. OPTI 201R Fall 2010 8-5 At an angle ! > 90 to each other: Figure 4.6 Two plane mirrors forming a dihedral edge with an angle greater than 90. # A ray in the principal projection plane is deviated by twice the dihedral angle minus 180 : 9 : ;7-180 (4.3) # @<&1 7 A BCD 6<& %0E3 5"=&%#& >%-2 &04< -6<&%) OPTI 201R Fall 2010 8-6 At an angle ! # 90 to each other: ("the homework problem") Figure 4.7 (a) Two perpendicular plane mirrors forming a roof, returning the light ray 180.Figure 4....
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OPTI 201R 10 L8 - OPTI 201R Fall 2010 8-1 Ch. 4 Mirrors and...

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