Refraction and Lenses

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Refraction and Lenses
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Refraction is the bending of light as it moves
from one medium to a medium with a different
optical density. This bending occurs as a result
of the speed of light changing at the interface
between the two media.
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Refraction
Notice the spoon appears to bend where it enters
the water.
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The light ray that hits the interface is called
the incident ray.
At the point where the incident ray hits the
interface, a normal (perpendicular) to the
surface should be drawn.
The angle between the incident ray and the normal
is called the angle of incidence.
The light ray that passes into the new medium is
called the refracted ray.
The angle between the refracted ray and the
normal is called the angle of refraction.
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Interface between 2 media
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As light strikes the interface between two media
with different optical densities at an oblique
(not 90o) angle, it changes speed and is
refracted.
As it moves from a less dense medium to a more
dense medium, it bends toward the normal
(perpendicular to the interface) and slows down.
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As it moves from a more dense medium to a less
dense medium, it bends away from the normal and
speeds up.
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If the light strikes the interface at a 90o
angle, it is not refracted and continues moving
in a straight line but its speed will change.
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When light passes through a parallel sided glass
figure, the emergent ray will be parallel to the
incident ray because the amount it is bent toward
the normal as it enters the glass is the same
amount it bends away from the normal as it leaves
the glass.
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glass
air
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• Light rays that strike the parallel sided glass
  figure perpendicular to the side will pass
  straight through the piece of glass without
  bending.

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Light is also refracted by the same rules when it
goes through an object that does not have
parallel sides. However, in this case, the
emergent ray will not be parallel to the incident
ray.
As the light ray enters the prism, it is moving
from a less dense to a more dense substance so it
is bent toward the normal.
As the light ray leaves the prism, it is moving
from a more dense to a less dense substance so it
is bent away from the normal.
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In the picture shown below, the light source is
on the right side. Notice the bending as the
light travels through the prism, when it leaves
the prism the white light has been separated into
its component colors. This separation is due to
the fact that each different wave length of light
moves at a slightly different speed in glass and
is therefore refracted at slightly different
amounts.
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Index of Refraction
The index of refraction of a substance is the
ratio of the speed light will travel in a vacuum
compared to the speed light will travel in the
substance .
ns c / vs
Ns is the index of refraction of the substance c
is the speed of light in a vacuum which is 3
108 m/s vs is the speed of light in the substance
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Snells Law
Shows the mathematical relationship between the
index of refraction and the amount that light is
refracted as it enters the substance.
n1sin?1 n2sin?2
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We are able to see most objects not because they
are emitting light but because they reflect
light. When you are looking into a pond, at many
angles you are able to see the fish below the
water but he is not exactly where you appear to
see him.
Object
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When the light reflected from the fish hits the
surface of the water at what is called the
critical angle, the light is refracted along the
surface of the water.
The critical angle occurs when the angle of
refraction is 90o. It can be calculated using
the equation
?1 sin-1 (n2 / n1)
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When light is reflected from a fish and it hits
the surface of the water at an angle greater than
the critical angle all of the light is reflected
back into the water and none is allowed to
escape. This is called internal reflection.
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Fiber Optic Cables
Light is transmitted along a fiber optic cable
due to the phenomenon of total internal
reflection.
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Internal Reflection
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The most common application of refraction in
science and technology is lenses. The kind of
lenses we typically think of are made of glass.
The basic rules of refraction still apply but due
to the curved surface of the lenses, they create
images.
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Types of Lenses
Convex lenses are also known as converging lenses
since they bring light rays to a focus.
Concave lenses are also known as diverging lenses
since they spread out light rays.
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Parts of a Lens
All lenses have a focal point (f). In a convex
lens, parallel light rays all come together at a
single point called the focal point. In a
concave lens, parallel light rays are spread
apart but if they are traced backwards, the
refracted rays appear to have come from a single
point called the focal point.
f
f
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The distance from the lens to the focal point is
called the focal length. Typically, a point is
also noted that is 2 focal lengths from the lens
and is labeled 2f.
The principle axis is a line which connects the
focal point and the 2f point and intersects the
lens perpendicular to its surface.
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Rules for Locating Refracted Images
1. Light rays that travel through the center of
the lens (where the principle axis intersects the
midline) are not refracted and continues along
the same path.
2. Light rays that travel parallel to the
principle axis, strike the lens, and are
refracted through the focal point (f).
3. Light rays that travel through the focal
point (f), strike the lens, and are refracted
parallel to the principle axis.
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All three of these light rays will intersect at
the same point if they are drawn carefully.
However, the image can be located by finding the
intersection of any two of these light rays.
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Real images are images that form where light rays
actually cross. In the case of lenses, that
means they form on the opposite side of the lens
from the object since light can pass through a
lens. Real images are always inverted (flipped
upside down).
Virtual images are images that form where light
rays appear to have crossed. In the case of
lenses, that means they form on the same side of
the lens as the object. Virtual images are always
upright.
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Images formed by Convex lenses
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Locating images in convex lenses
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Convex Lenses with the Object located beyond 2f
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Convex Lens Object located beyond 2f
2f
2f
f
f
Light rays that travel through the center of the
lens are not refracted and continue along the
same path.
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Convex Lens Object located beyond 2f
2f
2f
f
f
Light rays that travel parallel to the principle
axis, strike the lens, and are refracted through
the focal point (f).
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Convex Lens Object located beyond 2f
2f
Image Real Inverted Smaller Between f and 2f
2f
f
f
The image is located where the refracted light
rays intersect
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Convex Lenses with the Object located at 2f
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Convex Lens Object located at 2f
2f
2f
f
f
Light rays that travel through the center of the
lens are not refracted and continue along the
same path.
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Convex Lens Object located at 2f
2f
2f
f
f
Light rays that travel parallel to the principle
axis, strike the lens, and are refracted through
the focal point (f).
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Convex Lens Object located at 2f
2f
Image Real Inverted Same Size At 2f
2f
f
f
The image is located where the refracted light
rays intersect
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Convex Lenses with the Object located between f
and 2f
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Convex Lens Object located between f and 2f
2f
f
2f
f
Light rays that travel through the center of the
lens are not refracted and continue along the
same path.
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Convex Lens Object located between f and 2f
2f
f
2f
f
Light rays that travel parallel to the principle
axis, strike the lens, and are refracted through
the focal point (f).
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Convex Lens Object located between f and 2f
2f
Image Real Inverted Larger Beyond 2f
f
2f
f
The image is located where the refracted light
rays intersect
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Convex Lenses with the Object located at f
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Convex Lens Object located at f
2f
f
2f
f
Light rays that travel through the center of the
lens are not refracted and continue along the
same path.
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Convex Lens Object located at f
2f
f
2f
f
Light rays that travel parallel to the principle
axis, strike the lens, and are refracted through
the focal point (f).
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Convex Lens Object located at f
2f
f
2f
f
No image is formed. All refracted light rays are
parallel and do not cross
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Convex Lenses with the Object located between f
and the lens
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Convex Lens Object located between f and the lens
Light rays that travel through the center of the
lens are not refracted and continue along the
same path.
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Convex Lens Object located between f and the lens
Light rays that travel parallel to the principle
axis, strike the lens, and are refracted through
the focal point (f).
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Convex Lens Object located between f and the lens
2f
2f
f
f
These to refracted rays do not cross to the right
of the lens so we have to project them back
behind the lens.
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Convex Lens Object located between f and the lens
2f
Image Virtual Upright Larger Further away
2f
f
f
The image is located at the point which the
refracted rays APPEAR to have crossed behind the
lens
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Images formed by concave lenses
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Locating images in concave lenses
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Concave Lenses with the Object located anywhere
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Concave Lens Object located anywhere
2f
f
2f
f
Light rays that travel through the center of the
lens are not refracted and continue along the
same path.
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Concave Lens Object located anywhere
Light rays that travel parallel to the principle
axis, strike the lens, and are refracted through
the focal point (f).
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Concave Lens Object located anywhere
Image Virtual Upright Smaller Between f and the
lens
2f
f
2f
f
The image is located where the refracted light
rays appear to have intersected
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The eye contains a convex lens. This lens
focuses images on the back wall of the eye known
as the retina.
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The distance from the lens to the retina is fixed
by the size of the eyeball. For an object at a
given distance from the eye, the image is in
focus on the retina. Although the image on the
retina is inverted, the brain interprets the
impulses to give an erect mental image. If the
object moved closer to the eye and nothing else
changed the image would move behind the retina
the image would therefore appear blurred.
Similarly if the object moved away from the eye
the image would move in front of the retina again
appearing blurred. To keep an object in focus on
the retina the eye lens can be made to change
thickness. This is done by contracting or
extending the eye muscles. We make our lenses
thicker to focus on near objects and thinner to
focus on far objects.
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Someone who is nearsighted can see near objects
more clearly than far objects. The retina is too
far from the lens and the eye muscles are unable
to make the lens thin enough to compensate for
this. Diverging glass lenses are used to extend
the effective focal length of the eye lens.
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Someone who is farsighted can see far objects
more clearly than near objects. The retina is
now too close to the lens. The lens would have
to be considerable thickened to make up for this.
A converging glass lens is used to shorten the
effective focal length of the eye lens. Todays
corrective lenses are carefully ground to help
the individual eye but cruder lenses for many
purposes were made for 300 years before the
refractive behavior of light was fully understood.
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Lens Equation
(1/f) (1/do) (1/di)
f focal length do object distance di image
distance
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Lens Magnification Equation
M -(di / do) (hi / ho)
M magnification di image distance do object
distance hi image height ho object height
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Lens Sign Conventions
f for Convex lenses - for Concave Lenses di
for images on the opposite side of the lens
(real) - for images on the same side
(virtual) do always hi if upright
image - if inverted image ho always M
if virtual - if real image Magnitude of
magnification lt1 if smaller 1 if same
size gt1 if larger