Refraction is the change of direction of a light wave caused by a change in speed as the wave crosses a boundary between materials.

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Refraction is the change of direction of a light
wave caused by a change in speed as the wave
crosses a boundary between materials.
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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.
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The index of refraction is greater than one for
any material other than a vacuum.
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Snells 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 n1sinq1 n2sinq2.
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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.
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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.
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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.
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But when the angle of incidence is nearly 90,
most of the energy is reflected and little is
refracted.
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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?
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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 depthd is the actual depthn2 is the
medium of the observern1 is the medium of the
object
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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?
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Ex. 4 - A swimmer is under water and looking up
at the surface. Someone holds a coin in the air,
directly above the swimmers 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?
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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.
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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.
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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.
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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.
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At an incident angle called the critical angle
qC, the angle of refraction is 90.
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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.
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Total internal reflection can only occur when
light moves from a higher-index medium to a
lower-index medium.
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Using Snells law, this formula for the critical
angle can be obtainedsin qC n2sin
90/n1.Since sin 90 1, sin qC n2/n1 if
n1 gt n2.
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Ex. 5 - A beam of light is propagating through
diamond (n1 2.42) and strikes a diamond-air
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).
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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.
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Total internal reflection is also used in optical
fiber to keep the light rays within the fiber.
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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.
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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.
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Converging lens - convex lens, thicker in the
middle than at the edges.Diverging lens -
concave lens, thicker at the edges than in the
middle.
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The principal axis passes through the two centers
of curvature of the two surfaces of the lens.
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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.
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If rays do not pass through a principal focus, it
is a virtual focus.
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The positions of the foci on the principal axis
depend on the index of refraction of the lens.
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The focal length of a lens is the distance
between the optical center of the lens and the
principal focus.
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Parallel rays that are not parallel to the PA
are focused on the focal plane.
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Convex lenses form images like concave mirrors,
concave lenses form images like convex mirrors.
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Images formed by converging lensesCase 1
Object at an infinite distance.
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Case 2 Object at a finite distance beyond
the twice the focal length
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Case 3 Object at a distance equal to twice
the focal length
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Case 4 Object between one and two focal lengths
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Case 5 Object at principle focus
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Case 6 Object at a distance less than one
focal length away
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Diverging lenses
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