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Thin lenses - devices which refract light

(#6) form enlarged virtual upright images when d_o < f
(#5) do not form any image when d_o = f (parallel rays)
(#4) form real enlarged images when 2f < d_o < f
(#3) form real images that are the same size as the object when d_o = 2f
(#2) form real reduced images when d_o > 2f
(#1) form point images when d_o Þ ¥

thicker on the edges than in the center, concave
diverge light - principal focus is to the left
always form reduced virtual upright images

thin lens equation

d_o is always positive with a single lens
d_i is positive for real images, negative for virtual images
f is positive for converging lenses, negative for diverging lenses

magnification

thin lenses in close combination

power of a lens

measured in Diopters
focal length must be measured in meters

Lens-maker's equation

n₁ is the index of the lens
n₂ is the index of the surrounding medium
r₁ is the radius of curvature for the front surface (+ if convex, - if concave)
r₂ is the radius of curvature for the back surface (+ if convex, - if concave)
K_shape represents the shape of the lens which does not change when placed in different mediums

when drawing ray diagrams or using the thin-lens equation, work each lens separately
remember that the image of lens #1 is the object for lens #2
to calculate d_o for lens #2, subtract d_i for lens #1 from the total distance separating the lenses
the magnifications of the system is the product of the magnifications of each separate lens

ray diagram for microscope - virtual image formed by eyepiece

Refraction

Snell's Law

light bends towards the normal when it enters a more dense medium
light slows down when its travels through a more dense medium
the wavelength of light decreases as it travels through a more optically dense medium
the frequency of light is an invariant - it never changes