Review Sheet

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Thin lenses - devices which refract light

converging lenses in air (chart)

thicker in the center than on the edges, convex
converge light - principal focus is to the right
usually form real inverted images (review 6 cases)

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

diverging lenses in air (chart)

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

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


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)
Kshape represents the shape of the lens which does not change when placed in different mediums

double-lens systems

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 do for lens #2, subtract di 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

converging/converging and converging/diverging systems

converging/converging can form a final image that is either real and upright or virtual and inverted
converging/diverging form virtual inverted images

ray diagram for microscope - virtual image formed by eyepiece


index of refraction


c = 3 x 108 m/sec
n > 1

the index is a measure of a medium's optical density (photon interaction with electrons)
dispersion:  a medium's index of refraction is actually frequency dependent (spectrum)

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

Copyright 1997-2021
Catharine H. Colwell
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Mainland High School
Daytona Beach, FL 32114