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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.
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
 i > r
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
 i
 r
 i <  r
An object’s 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 a 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
m/s) / v
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.
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 Snell’s Law.
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
Click here, here,
and here to view
simulations of Snell’s
View an analytical derivation
of the geometrical
relationship here.
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
These lenses converge light to a real focus.
Diverging Lenses - thicker at edge than in middle
double 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 material’s index of refraction
and on the shape of the lens.
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
di/do = si/so.
Click here, here, and here to view
simulations showing image formation
in converging and diverging lenses
using these three important rays.
The PhET 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
The image characteristics depend on
the object’s position with respect
to one and two focal lengths
(1f and 2f) away from the lens.
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
The simulation linked to the optics applets
here shows image formation in all
types of lenses and curved mirrors.
Learn more about image characteristics here.
Images formed by diverging lenses are always:
located in front of the lens between the
focus and the lens
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