Refraction
As the speed of light is reduced in
the slower medium, the wavelength
is shortened proportionately. The
frequency is unchanged; it is a
characteristic of the source of the
light and unaffected by medium
changes.
Refraction of Light
Refraction is the bending of a
wave when it enters a medium
where it's speed is different.
The refraction of light when it
passes from a fast medium to a
slow medium bends the light
ray toward the normal to the
boundary between the two
media. The amount of bending
depends on the indices of
refraction of the two media
and is described quantitatively
by Snell's Law.
INDEX OF REFRACTION
The speed of all
electromagnetic
radiation in vacuum is
the same,
approximately 3×108
meters per second,
and is denoted by c.
Therefore, if v is the
phase velocity of
radiation of a specific
frequency in a
specific material, the
refractive index is
given by
This number is typically greater
than one: the higher the index
of the material, the more the
light is slowed down.
Because the Refractive Index
for a given substance at a
given temperature and
pressure is a constant,
Refractive Indices are used in
the real world to determine
everything from the
percentage of water in a
sample of honey to the
composition and purity of
gemstones.
Snell's law is used to calculate how much refraction occurs.
This is determined from the refractive index (RI) and the
angle of incidence (i).
Rays move towards
the normal when
the ray slows down
and away from the
normal when the ray
speeds up
Image Formation
Total Internal Reflection
When light is incident
upon a medium of lesser
index of refraction, the
ray is bent away from the
normal, so the exit angle
is greater than the
incident angle. Such
reflection is commonly
called "internal
reflection". The exit
angle will then approach
90° for some critical
incident angle qc , and for
incident angles greater
than the critical angle
there will be total
internal reflection
The field of fiber optics
depends upon the total
internal reflection of light
rays traveling through tiny
optical fibers. The fibers
are so small that once the
light is introduced into the
fiber with an angle within
the confines of the
numerical aperture of the
fiber, it will continue to
reflect off the walls of
the fiber and thus can
travel long distances in the
fiber. Bundles of such
fibers can accomplish
imaging of otherwise
inaccessible areas.
If a luminous object is
placed at a distance
greater than the focal
length away from a convex
lens, then it will form an
inverted real image on the
opposite side of the lens.
The image position may be
found from the lens
equation or by using a ray
diagram.
Real Image Formation
Virtual Image Formation
Refraction Rule for a Converging Lens
Any incident ray traveling parallel to the
principal axis of a converging lens will refract
through the lens and travel through the focal
point on the opposite side of the lens.
Refraction Rules for a Converging Lens
Any incident ray traveling parallel to the principal axis of a
converging lens will refract through the lens and travel through
the focal point on the opposite side of the lens.
Any incident ray traveling through the focal point on the way to
the lens will refract through the lens and travel parallel to the
principal axis.
Refraction Rule for a Diverging Lens
Any incident ray traveling parallel to the principal axis of a
diverging lens will refract through the lens and travel in line with
the focal point (i.e., in a direction such that its extension will pass
through the focal point).
Refraction Rules for a Diverging Lens
Any incident ray traveling parallel to the principal axis of a
diverging lens will refract through the lens and travel in line
with the focal point (i.e., in a direction such that its extension
will pass through the focal point).
Any incident ray traveling towards the focal point on the way
to the lens will refract through the lens and travel parallel to
the principal axis.
Refraction Rules for a Converging Lens
Any incident ray traveling parallel to the principal axis of a
converging lens will refract through the lens and travel through the
focal point on the opposite side of the lens.
Any incident ray traveling through the focal point on the way to the
lens will refract through the lens and travel parallel to the principal
axis.
An incident ray which passes through the center of the lens will in
affect continue in the same direction that it had when it entered the
lens.
Refraction Rules for a Diverging Lens
Any incident ray traveling parallel to the principal axis of a
diverging lens will refract through the lens and travel in line
with the focal point (i.e., in a direction such that its extension
will pass through the focal point).
Any incident ray traveling towards the focal point on the way
to the lens will refract through the lens and travel parallel to
the principal axis.
An incident ray which passes through the center of the lens
will in affect continue in the same direction that it had when
it entered the lens.
Ray Diagram for Object Located in Front of the Focal Point
Ray Diagram for Object Located at the Focal Point
Converging Lenses - Object-Image Relations
Step-by-Step Method for Drawing Ray Diagrams
Diverging Lenses - Object-Image Relations
The Mathematics of Lenses
Sign Conventions
f is + if the lens is a double convex lens
(converging lens)
f is - if the lens is a double concave lens
(diverging lens)
di is + if the image is a real image and located on
the opposite side of the lens.
di is - if the image is a virtual image and located
on the object's side of the lens.
hi is + if the image is an upright image (and
therefore, also virtual)
hi is - if the image an inverted image (and
therefore, also real)
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