Transcript index of refraction

Refraction is the
change of direction of a
light wave caused by a
change in speed as the
wave crosses a
boundary between
materials.
The index of refraction
of a material is the
speed of light in a
vacuum divided by the
speed of light in the
material, n = c/v.
The index of
refraction is greater
than one for any
material other than
a vacuum.
Snell’s law of refraction - When
light travels from a material with
refractive index n1 into a material
with refractive index n2, the
refracted ray, incident ray, and
normal all lie in the same plane.
The angle of refraction q2 is related
to the angle of incidence q1 by
n1•sinq1 = n2•sinq2.
Ex. 1 - A light ray strikes an
air/water surface at an angle of
46° with respect to the normal.
The refractive index for water is
1.33. Find the angle of
refraction when the direction of
the ray is (a) from air to water
and (b) from water to air.
When a ray of light passes
obliquely from a medium of lower
index of refraction to one of higher
index of refraction, it is bent toward
the normal to the surface. A ray of
light passing from a medium of
higher index of refraction to one of
lower index of refraction is bent
away from the normal to the
surface.
When light energy is
simultaneously reflected and
refracted at a boundary, the
total energy must remain
constant. When light is
directed along the normal,
most all is refracted and little
is reflected.
But when the angle
of incidence is nearly
90°, most of the
energy is reflected
and little is refracted.
Ex. 2 - A searchlight on a yacht
is used at night to illuminate a
sunken chest. The chest in
water 3.3 m deep, and the
incident ray strikes the water at
a point 2.0 m from a point
directly above the chest. At what
angle of incidence q1 should the
light be aimed?
The chest (or any object) is seen
as being at a depth less than the
actual depth. This virtual image is
at an apparent depth that can be
found using this formula:
d’ = d(n2/n1).
d’ is the apparent depth
d is the actual depth
n2 is the medium of the observer
n1 is the medium of the object
Ex. 3 - A swimmer is
treading water at the
surface of a 3.00-m-deep
pool. She sees a coin on
the bottom directly below.
How deep does the coin
appear to be?
Ex. 4 - A swimmer is under water
and looking up at the surface.
Someone holds a coin in the air,
directly above the swimmer’s eyes.
To the swimmer, the coin appears
to be at a certain height above the
water. Is the apparent height of the
coin greater than, less than, or the
same as its actual height?
A transparent slab of material
displaces a ray of light. The
amount of the displacement
depends on the angle of
incidence, the thickness of the
slab, and its refractive index.
The ray that enters and the ray
that exits are parallel if the
surfaces of the slab are parallel.
When a light wave enters
a material of higher index
of refraction, the speed
decreases, the wavelength
decreases, but the frequency
remains unchanged.
The frequency of a light
wave is constant.
When light passes from a
medium of larger index of
refraction to a medium of
lower index of refraction,
the refracted ray bends
away from the normal.
The angle of incidence is
smaller than the angle of
refraction. As the angle of
incidence increases, the
angle of refraction does also;
therefore, the angle of
refraction reaches 90°
before the angle of incidence.
At an incident angle
called the critical
angle qC, the angle
of refraction is 90°.
At an angle of incidence
above the critical angle
all the incident light is
reflected at the boundary
back into the medium; this
is total internal reflection.
Total internal
reflection can only
occur when light
moves from a higherindex medium to a
lower-index medium.
Using Snell’s law, this
formula for the critical
angle can be obtained:
sin qC = n2•sin 90°/n1.
Since sin 90° = 1,
sin qC = n2/n1 if n1 > n2.
Ex. 5 - A beam of light is
propagating through diamond
(n1 = 2.42) and strikes a diamondair interface at an angle of
incidence of 28°. (a) Will part of the
beam enter the air (n2 = 1.00) or
will the beam be totally reflected at
the interface? (b) Repeat part (a),
assuming that the diamond is
surrounded by water (n2 = 1.33).
Optical instruments like
binoculars and telescopes use
prisms and total internal
reflection to redirect rays of
light. Mirrors reflect a
percentage of light; total internal
reflection is more efficient
because it is 100% reflection.
Total internal
reflection is also
used in optical fiber
to keep the light
rays within the fiber.
A prism bends light as it
enters and as it leaves
the prism. Its triangular
shape causes the light to
be refracted twice in the
same direction.
The index of refraction is
different for different colors.
Different wavelengths are
refracted different amounts,
so the light is separated into
a spectrum of colors; this is
called dispersion.
Converging lens - convex
lens, thicker in the
middle than at the edges.
Diverging lens - concave
lens, thicker at the edges
than in the middle.
The principal axis
passes through the
two centers of
curvature of the two
surfaces of the lens.
Rays that are parallel
to the PA converge at
the principal focus of
the lens.
If they actually pass
through this point
it is a real focus.
If rays do not
pass through a
principal focus, it
is a virtual focus.
The positions of the
foci on the principal
axis depend on the
index of refraction
of the lens.
The focal length of a
lens is the distance
between the optical
center of the lens
and the principal
focus.
Parallel rays that
are not parallel
to the PA are
focused on the
focal plane.
Convex lenses form
images like concave
mirrors, concave
lenses form images
like convex mirrors.
Images formed by converging lenses:
Case #1
Object at an infinite distance.
Case #2 Object at a finite distance
beyond the twice the focal length
Case #3 Object at a distance
equal to twice the focal length
Case #4 Object between one and
two focal lengths
Case #5 Object at principle focus
Case #6 Object at a distance less
than one focal length away
Diverging lenses