23.1)Flat Mirrors

  O is the position of the source Object.
  
  p is the distance from the object to mirror.
  
  I is the reflected Image of the object.
  
  q is the distance from the Image to the mirror.
  
  In flat mirrors, p=q.
  
  h = object height
  
  h' = image height
  
  M ≡ (image height)/(object height) = h'/h
  
  M is the Lateral Magnification.
  
  For flat mirrors, M is 1.
  
  
23.2) Images formed by spherical mirrors

  Concave Mirror - the object and image are inside the curve.
  
  C = Center of curvature
  
  V = midpoint of mirror
  
  R = Radius = distance from V to C
  
  M = h'/h = -q/p
  
  Where M is the Lateral Magnification.
  
  1/p + 1/q = 2/R
  
  If the Object is very far from the mirror, the incoming rays are essentially
  parallel causing a Focal point to be created.
  
  F = Focal point
  
  f = distance from V to F
  
  f = R/2
  
  1/p + 1/q = 1/f
  
23.3) Convex mirrors and sign conventions

  The equations for Concave mirrors apply to Convex mirrors as well.
  
  Sign Conventions
  
  p is + if the object is in front of the mirror (real)
  p is - if the object is behind the mirror (virtual)

  q is + if the image is in front of the mirror (real)
  q is - if the image is behind the mirror (virtual)  
  
  Both f and R are + if the curvature is in front of the mirror (concave)
  Both f and R are - if the curvature is behind the mirror (convex)
  
  If M is positive, Image is upright
  If M is negative, Image is inverted.
  
  Note:  In the real world, it is impossible for p to be negative for a 
  non-refracting mirror.
  
23.4) Images Formed by Refraction

  n1 = index of refraction of material 1
  
  n2 = index of refraction of material 2
  
  n1/p + n2/q = (n2 - n1 )/ R
  
  M = h'/h = -(n1 q)/(n2 p)
  
  The same rules for mirrors also apply to refracting reflective surfaces.
  
22.5) The Law of Refraction
  
  A mirage is a classic example of naturally occurring refraction.  The 
  refraction is due to the fact the air has different indices of refraction
  at different temperatures.
  

23.6) Thin Lenses  

  Converging Lenses - have positive focal lengths and are thickest in the 
  middle.
  
  Diverging Lenses - have negative focal lengths and are thickest at the edges.
  
  The same equations for convex and concave mirrors apply to thin lenses.
  In addition:
  
  1/f = (n-1)(1/R1 - 1/R2)
  
  Where R1 is the radius of curvature at the front of the lens and R2 is the
  radius of curvature at the back of the lens.
  
HW 8:
p. 781 M.C. # 1,   
p. 781 C.Q. #2, 
p. 782 #1
p. 783 #4
p. 783 #22
p. 784 #27