Reflection and Mirrors

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Reflection and Mirrors Refraction and Lenses
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The Law of Reflection

• The angle of incidence equals the angle of
  reflection.

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The Law of Reflection

• When light strikes a surface it is reflected.
• The light ray striking the surface is called the
  incident ray.
• A normal (perpendicular) line is then drawn at
  the point where the light strikes the surface.
• The angle between the incident ray and the normal
  is called the angle of incidence.
• The light is then reflected so that the angle of
  incidence is equal to the angle of reflection.
• The angle of reflection is the angle between the
  normal and the reflected light ray.

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Mirror
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The incident ray, normal, and reflected ray are
all in the same plane.
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Regular reflection occurs when light is reflected
from a smooth surface. When parallel light rays
strike a smooth surface they are reflected and
will still be parallel to each other.
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Diffuse reflection occurs when light is reflected
from a rough surface. The word rough is a
relative term. The surface is rough at a
microscopic level. For example, an egg is a
rough surface. When parallel light rays strike a
rough surface, the light rays are reflected in
all directions according to the law of reflection.
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Types of Mirrors
Convex mirrors are made from a section of a
sphere whose outer surface was reflective. Convex
mirrors are also known as diverging mirrors since
they spread out light rays. They are typically
found as store security mirrors.
Concave mirrors are made from a section of a
sphere whose inner surface was reflective. Concave
mirrors are also known as converging mirrors
since they bring light rays to a focus. They are
typically found as magnifying mirrors
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Plane Mirrors have a flat surface. The mirror
hanging on the wall in your bathroom is a plane
mirror.
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Real images are images that form where light rays
actually cross. In the case of mirrors, that
means they form on the same side of the mirror as
the object since light can not pass through a
mirror. 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
mirrors, that means they form behind the
mirror. Virtual images are always upright.
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Plane Mirror
In a plane mirror the object is the same size,
upright, and the same distance behind the mirror
as the object is in front of the mirror.
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Images in a plane mirror are also reversed left
to right.
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Curved Mirrors
The center of curvature also known as radius of
curvature (C) of a curved mirror is located at
the center of the sphere from which it was made.
The focal point (f) is located halfway between
the mirrors surface and the center of curvature.
C 2f
The principle axis is a line that passes through
both the center of curvature (C) and the focal
point (f) and intersects the mirror at a right
angle.
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Rules for Locating Reflected Images
1. Light rays that travel through the center of
curvature (C) strike the mirror and are reflected
back along the same path.
2. Light rays that travel parallel to the
principle axis, strike the mirror, and are
reflected back through the focal point (f).
3. Light rays that travel through the focal
point (f), strike the mirror, and are reflected
back 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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Locating images in concave mirrors
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Concave Mirror with the Object located beyond C
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Concave Mirror Object beyond C
Light rays that travel through the center of
curvature (C) hit the mirror and are reflected
back along the same path.
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Concave Mirror Object beyond C
Light rays that travel parallel to the principle
axis, strike the mirror, and are reflected back
through the focal point (f).
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Concave Mirror Object beyond C
Light rays that travel through the focal point
(f), strike the mirror, and are reflected back
parallel to the principle axis.
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Concave Mirror Object beyond C
Image Real Inverted Smaller Between f and C
The image is located where the reflected light
rays intersect
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Concave Mirror with the Object located at C
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Concave Mirror Object at C
Light rays that travel parallel to the principle
axis, strike the mirror, and are reflected back
through the focal point (f).
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Concave Mirror Object at C
Light rays that travel through the focal point
(f), strike the mirror, and are reflected back
parallel to the principle axis.
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Concave Mirror Object at C
Image Real Inverted Same Size At C
The image is located where the reflected light
rays intersect
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Concave Mirror with the Object located between f
and C
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Concave Mirror Object between f and C
Light rays that travel through the center of
curvature (C) hit the mirror and are reflected
back along the same path.
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Concave Mirror Object between f and C
Light rays that travel parallel to the principle
axis, strike the mirror, and are reflected back
through the focal point (f).
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Concave Mirror Object between f and C
Light rays that travel through the focal point
(f), strike the mirror, and are reflected back
parallel to the principle axis.
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Concave Mirror Object between f and C
Image Real Inverted Larger Beyond C
The image is located where the reflected light
rays intersect
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Concave Mirror with the Object located at f
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Concave Mirror Object at f
Light rays that pass through the center of
curvature hit the mirror and are reflected back
along the same path.
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Concave Mirror Object at f
Light rays that travel parallel to the principle
axis, strike the mirror, and are reflected back
through the focal point (f).
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Concave Mirror Object at f
No image is formed. All reflected light rays are
parallel and do not cross
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Solar "Death Ray"

• http//www.youtube.com/watch?vTtzRAjW6KO0

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Concave Mirror with the Object located between f
and the mirror
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Concave Mirror Object between f and the mirror
Light rays that travel through the center of
curvature (C) hit the mirror and are reflected
back along the same path.
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Concave Mirror Object between f and the mirror
Light rays that travel through the focal point
(f), strike the mirror, and are reflected back
parallel to the principle axis.
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Concave Mirror Object between f and the mirror
Light rays that travel parallel to the principle
axis, strike the mirror, and are reflected back
through the focal point (f).
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Concave Mirror Object between f and the mirror
Image Virtual Upright Larger Further away
The image is located where the reflected light
rays intersect
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Locating images in convex mirrors
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Convex Mirror with the Object located anywhere in
front of the mirror
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Convex Mirror Object located anywhere
Light rays that travel through the center of
curvature (C) hit the mirror and are reflected
back along the same path.
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Convex Mirror Object located anywhere
Light rays that travel parallel to the principle
axis, strike the mirror, and are reflected back
through the focal point (f).
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Convex Mirror Object located anywhere
Light rays that travel through (toward) the focal
point (f), strike the mirror, and are reflected
back parallel to the principle axis.
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Convex Mirror Object located anywhere
Image Virtual Upright Smaller Behind mirror,
inside f
The image is located where the reflected light
rays intersect
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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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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 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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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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• Concave Lenses arent on STAAR, they wont be on
  our test and can be omitted from homework
  assignments.

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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 two 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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The Lens Formula

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• Object distance do
• Image distance di
• Focal length f

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Sign Conventions

• 1. All distances are measured from center of
  optical device2. Distances of real objects and
  images are positive" virtual " " negative
  (example of a virtual object?)3. Heights of
  object and images are positive when upright and
  negative when inverted.
• 4. Focal lengths of converging(convex) lenses
  are positive diverging lenses have negative
  focal lengths.

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do
di
f
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Sample Problem p.575
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Di
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p. 576 problems 1,2 and 3 just find di, not
magnification
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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.
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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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