refraction. optical density inverse measure of speed of light through transparent medium light...
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Refraction
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Optical Density
Inverse measure of speed of light through transparent medium
Light travels slower in more dense mediaPartial reflection occurs at boundary with
more dense mediumIf incident angle not 90 degrees, refraction
occurs
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Optical Refraction
Bending of light rays as they pass obliquely from one medium to another of different optical density
Angle of refraction measured to normal from refracted ray
Passing from lower to higher density, light refracted towards normal; high to low, away from normal
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Index of Refraction
Ratio of speed of light in a vacuum (c) to its speed in a substance
n =c/vMeasured by refractometer, used to test
purity of substance
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Snell’s Law
Relates index of refraction to the angle of refraction
Between any two media ni(sin i) = nr(sin r)
Since nair = 1.00, for light passing from air into another transparent medium,
n = sin i / sin r
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Atmospheric Refraction
Causes gradual curve of light from stars and sun
Creates mirages that look like wet spots on roads
Makes sun visible 2-3 min. before sunrise and after sunset
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Mirage Formation
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Highway Mirage
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Laws of Refraction
Incident ray, refracted ray & normal line all lie in same plane
Index of refraction for homogeneous medium is constant, independent of incident angle
Oblique ray passing from low to high optical density is bent towards normal and vice versa
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Dispersion
Transparent media react differently to different wavelengths, slowing short waves more than long waves
Different wavelengths are refracted to a different degree, violet more than red
Causes spreading of the light according to wavelength (frequency) - rainbow
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Dispersion
Prisms, water drops readily disperse light due to non-parallel surfaces
Rainbows created by refraction through many drops
Each color produced by a set of drops at a certain angle from the eye
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Dispersion in Raindrops
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Rainbow Physics
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Total Reflection
At media boundary, light from denser medium refracted back into it, rather than exiting into less dense medium
Critical angle: incident angle that produces refracted angle of 90 degrees
At critical angle, refracted ray parallel to media boundary
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Total Reflection
From Snell’s law: n = sin 90o/sin ic so
sin ic = 1/n
Critical angle for water is 48.5 deg., for diamond it is 24 deg.
If incident angle > critical angle, total reflection occurs
Causes diamond’s sparkle, fiber optics
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Total Internal Reflection
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Fiber Optics
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Lenses
Transparent object with nonparallel surfaces, at least one of which is curved
Usually glass or plastic but can be water, air, other transparent solid, liquid or gas
Converging: thicker in middle, converges (focuses) rays
Diverging: thinner in middle, diverges (spreads) rays
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Lens Terms
Each side of lens has center of curvature and focus
Real focus (converging lens) where light rays pass through
Real image forms on same side of lens as real focus, opposite side of object
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Lens Terms
Virtual focus (diverging or converging) where light rays appear to have originated
Virtual image forms on same side of lens as virtual focus and object
Focal length: distance from center of lens to focal point; depends on curvature and index of refraction of lens
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Mirrors & Lenses: Differences
Secondary axes pass through center of lensPrincipal focus usually near C; use 2F
instead of C in ray diagramsReal images on opposite side of lens as
object, virtual images on same sideConvex lenses are like concave mirrors,
concave lenses like convex mirrors
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Images of Converging Lenses
Object at infinite distance forms point image at F on opposite side
Object at finite distance > 2F forms real, reduced image between F and 2F on opposite side
Object at 2F forms real, same size image at 2F on opposite side
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Images of Converging Lenses
Object between F and 2F forms real, magnified image beyond 2F on opposite side
Object at F forms no image, rays are parallel
Object between F and lens forms enlarged, virtual image on same side (magnifying glass)
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Images of Diverging Lenses
Always virtual, erect, reduced sizeOften used to neutralize or minimize effect
of converging lens (glasses)
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Lens Equations
1/f = 1/do + 1/di
hi / ho = di / do
For simple magnifier, magnification
M = hi / ho = di / do
for normal vision, di = 25 cm, so
M = 25 cm/f (f - focal length)
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f-numbers
Ratio of focal length to aperture (effective diameter), used to rate camera lenses
Determines light gathering power of lens“Fast” lenses have low f-numbers, gather
more light, need shorter exposure timesSince area of lens is prop. to square of
diameter, f-2 lens is 4 times faster than f-4, 16 times faster than f-8
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The Microscope
Objective lens forms enlarged, real imageEyepiece magnifies image of objective
producing greatly magnified, inverted, virtual image
Objective power = tube length/focal lengthTotal magnification M=25length/fe fo ( all
in cm)
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Telescopes
Reflectors have one converging mirror and a converging eyepiece lens
Refracting telescopes have large objective lens instead of a mirror
Object at great distance means small, real image is produced by objective mirror or lens
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Telescopes
Eyepiece lens enlarges objective image producing magnified, inverted, virtual image
Large telescopes are reflectors due to size and expense of large lens
Binoculars, terrestrial telescopes use extra lens or prism to invert image to upright position
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The Eye
Cornea and lens work together to focus light on retina producing inverted, small image
Brain circuitry inverts image so it seems right side up
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Vision Correction
Nearsighted means light focuses in front of retina—corrected with diverging lens
Farsighted means light would focus behind retina—corrected with converging lens
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Cameras
Cameras focus light on the focal plane where the film is located
Produce real, inverted, smaller image, like the eye
Some cameras use a diverging lens for a viewfinder
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Lens Aberrations
Spherical aberration: like mirrors, light passing through edges not focused at same point as through center - correct with lens combination
Chromatic aberration: different colors refracted differently, focus at different points - correct with lens coatings, lenses of different materials