the change of direction of a ray of light

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the change of direction of a ray of light as it
passes obliquely from one medium into another of
different transmission speed
Optical Density of a medium refers to the speed
of light in that medium.
It does not necessarily Correspond to the Mass
density of that material.
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When light travels from a less dense to more
dense medium (light slows down), the ray is
refracted toward the normal.
Example light slows down when it passes from
air
into water
n
i
i
gt
r
air
water
r
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When light travels from a more dense medium to a
less dense medium (light speeds up), the ray is
refracted away from the normal.
Example light speeds up when passing from
glass into air
air
i
n
r
glass
i
r
lt
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An objects ability to decrease the speed of
light, and therefore cause refraction, is given
by its index of refraction. By definition
the index of refraction of any transparent
substance is equal to the speed of light in a
vacuum divided by the speed of light in that
substance.
n c / v
n (3 x 108 m/s) / v
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The table to the left shows values of the index
of refraction for some common substances. The
larger the index of refraction, the slower that
light travels through the substance.
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The angles of incidence and refraction are
related in such a way that n (sin i)/(sin
r), where i angle of incidence and r
angle of refraction whenever light passes from a
vacuum into the substance.
In general, for light passing from medium 1 into
medium 2,
n1 sin q1 n2 sin q2
This relationship is known as Snells Law.
q1
n1
n2
q2
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Total Internal Reflection may occur when light
enters a new medium and speeds up (bends away
from the normal). Investigate here. The
maximum angle of incidence in which light may
enter air from another substance and not undergo
total internal refraction is known as the
critical angle, and is related to the index of
refraction of the substance by
sin qc 1/n
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Click here, here,
and here to view
simulations of Snells
Law. View an analytical derivation of the
geometrical relationship here. Investigate
total internal reflection here.
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LENS
any transparent object having two nonparallel
curved surfaces or one plane surface and one
curved surface
Converging Lenses - thicker in middle than in the
edge
double convex
plano-convex
concavo-convex
These lenses converge light to a real focus.
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Diverging Lenses - thicker at edge than in middle
double concave
plano-concave
convexo-concave
These lenses diverge light from a virtual focus.
The focal length of a lens is generally
NOT half-way between the center of curvature and
the vertex of the lens, but it depends on the
lens materials index of refraction and on the
shape of the lens.
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Ray Diagrams
Converging and Diverging Lenses
1. Rays passing through the optical center pass
straight through without refraction. 2. Incident
rays parallel to the principal axis refract
through the focus or diverge away from the
focus. 3. Rays passing through or toward the
focus refract parallel to the principal axis.
Just like mirrors, 1/f 1/do 1/di and di/do
si/so.
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Click here, here, and here to view simulations
showing image formation in converging and
diverging lenses using these three important rays.
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The simulation linked here shows image formation
in a converging lens. Learn more about image
characteristics here.
Images formed by converging lenses may be 1.
real, virtual, or non-existent 2. upright or
inverted 3. reduced, enlarged, or same size 4. in
front or behind the lens
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The image characteristics depend on the objects
position with respect to one and two focal
lengths (1f and 2f) away from the lens.
2f
f
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object is beyond two focal lengths image is
real, inverted, and reduced
object is exactly twice the focal length image
is real, inverted, and the same size
object between one and two focal lengths image
is real, inverted, and enlarged
object is on the focus no image rays reflect
parallel
object is inside the focus image is virtual,
upright, and enlarged
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The simulation linked here shows image formation
in a diverging lens. Learn more about image
characteristics here.
Images formed by diverging lenses are always 1.
virtual 2. upright 3. reduced 4. located in front
of the lens between the focus and the lens
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• General Image Trends
• real images are always inverted
• virtual images are always upright
• real images are always behind the lens
• virtual images are always in front
• of the lens
• negative image distance means
• virtual image
• positive image distance means real image
• real images may be projected onto a screen
  virtual images may not