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Equations
n = c / v n = l_{vac} / l_{med} n_{1} sin q_{1} = n_{2} sin q_{2} v_{w} = fl
Converging Lenses  Diverging Lenses  
shape  "caved in"  "bowed out"  
position of principal focus 
F is "behind the lens" on the opposite side of the lens as the incoming light 
F is "in front of the
lens" on the same side of the lens as the incoming light 

image position 
1/d_{o} + 1/d_{i} = 1/f do is always positive d_{i} is positive if real d_{i} is negative if virtual f is positive (convex) 
1/d_{o} + 1/d_{i} = 1/f do is always positive d_{i} is always negative (virtual) f is negative (concave) 

image
properties 
varies with d_{o} six case ray diagrams

virtual, upright, M < 1 ray diagrams


magnification  M =  d_{i} / d_{o}  =  I / O   M =  d_{i} / d_{o}  =  I / O   
rays  #1 top of
the object, parallel to the axis, strikes the lens, refracts through F #2 top of the object, passes through the center of the lens unbent #3 top of the object, aims for F', strikes the lens, refracts parallel to the axis 
#1 top of
the object, parallel to the axis, strikes the lens, refracts through F
(dot in line to F) #2 top of the object, passes through the center of the lens unbent #3 top of the object, aims for F', strikes the lens, refracts parallel to the axis (dot back refracted ray) 
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