Reflection and refraction indices sparkling diamonds

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Reflection and refraction indices - sparkling
diamonds

• For a light beam incident upon a boundary between
  two transparent media at 90

• Glass n1 1.5,

• Diamond n1 2.4,

What happens if the light is not coming at the
angle of 90?
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What happens if the light is not coming at the
angle of 90?
The light coming at 90 corresponds to the angle
of incidence q 0. As a rule, at greater angles
of incidence more light gets reflected. Look at
your watch glass at a grazing angle! It will act
as a pretty good mirror!
Is there any dependence on polarization of
light? How is the reflected wave created in the
first place? How does it depend on the medium the
wave is going to?
The primary source of the reflected wave are
oscillating charges in the medium the light is
going to. Therefore the direction of
polarization corresponds to the direction of
oscillation of the charges.
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EM Waves by an Antenna

• Two rods are connected to an ac source, charges
  oscillate between the rods (a)
• As oscillations continue, the rods become less
  charged, the field near the charges decreases and
  the field produced
• at t 0 moves away from the rod (b)
• The charges and field reverse (c)
• The oscillations continue (d)

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How does that apply to the light waves?
At a particular angle of incidence, called the
Brewster angle, the light polarized in the plane
on incidence-reflection-refraction does not get
reflected at all!You do not need any special
coating just appropriate polarization.
Brewster angle corresponds to the situation, when
the reflected wave is supposed to go in the
direction of polarization of the wave inside
glass (2nd medium).The directions of the
reflected and refracted waves are set by laws of
reflection/refraction.The charges inside glass
oscillate in the direction of polarization (E)
and cannot radiate the reflected wave.
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Brewster angle corresponds to the situation,
when the reflected wave is supposed to go in the
direction of polarization of the wave inside
glass (2nd medium).The charges inside glass
oscillate in the direction of polarization (E)
and cannot radiate the reflected wave.
Brewster angle can be found from the condition
that the refracted ray goes at 90 to the
reflected ray. Therefore, angle of incidence
angle of refraction 90
Under what conditionsis the polarizing angle
smaller than 45º?
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At a particular angle of incidence, called
Brewster angle, the light polarized in the plane
on incidence-reflection-refraction does not get
reflected at all!
By the same token, if the incident light is
unpolarized, only the component perpendicular to
the plane of incidence gets reflected.Therefore,
the reflected light is perfectly polarized
perpendicularto the plane of incidence-reflection
-refraction
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A shop window photographed at the Brewster angle
without and with polarization filter.
Practical conclusionsIf you need to view
objects through glass (camera, telescope etc),
try to look at the Brewster angle for air-glass -
56?.Do not forget a good polarization filter
(polarizer)!
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Mirror as an image forming device
Image a pattern of light that provides visual
representation of reality
Image - the optical counterpart of an object
produced by an optical device as a lens or mirror
a likeness of an object produced on a
photographic material.
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Image formation in a plane mirror.
The image is always there, in a well defined
position, whether you look at it or not.The
image is formed behind the mirror at a distance
equal to the distance from the object, and has
size equal to the size of the object.It is a
virtual image, since there is no light in the
image location. The light only appears to come
from there.
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How exactly do we see (images of the) objects in
a mirror?Pretty much the same way as when we
are looking at the objects directly!And there
are always many more rays emanating from an
object than getting to our eyes.Thats how
different people can see the same object/image
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In the overhead view of the figure below, the
image of the stone seen by observer 1 is at C.
Where does observer 2 see the image at A, at
B, at C, at E, or not at all?
Position of an image is defined just as well as
position of the object! A little geometry
demonstrates that its location is independent of
the position of the observer!
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Looking into a mirror at yourselfFor an
unobstructed, complete view you only need a
mirror, which is a half of your height.
Question What is going to happen to your image
in the mirror if you walk away from it?
Answer Nothing other than it will appear to be
further away, twice the distance of that from
you to the mirror.
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Mirrors are known to turn left into right, that
is to make the image of your left hand look as
your right hand.
It is this effect that gives rise to the
expression A Mirror Image
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The mirrors actually do a very special
transformation, known as inversion, which cannot
be reduced to translations and rotations
Maybe to turning inside out?...
Chiral objects and chiral molicules
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Curved Mirrors - Parabolic Mirrors
Properties of a parabolic mirror Any ray
parallel to the mirror axis reflects through
the focal point A point source of light at the
focus will emerge from the mirror in a beam of
parallel rays
They can be used to concentrate light to high
intensities solar energy They can be used to
design light sources, head lights, flashlights,
etc.
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Curved Mirrors - Spherical Mirrors
Spherical mirrors are easier to make Over a small
region near the apex they are the same as a
parabolic mirror Deviation from parabolic causes
spherical aberration (more later)
It can be shown, an exercise for the student,
that the distance to the center of curvature is
twice the focal length
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Curved Mirrors - Spherical Mirrors
Spherical mirrors form images
(a) Object beyond C, image is real, reduced, and
inverted. (b) Object between C and F, image is
real, magnified, and inverted. (c) Object inside
F, image is virtual, magnified, and upright.
Question Can a parabolic mirror form an image?
Answer Of course! The above applies, replace C
with 2F
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Curved Mirrors - Parabolic Mirrors
Parabolic mirrors form images
The image of the pig is so real it seems that
you could reach out and touch it!
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Curved Mirrors - Spherical Mirrors
Spherical mirrors form images

• Any ray parallel to mirror axis reflects through
  the focal point
• Any ray that passes through the focal point
  reflects parallel to the axis
• Any ray that strikes the center of the mirror
  reflects symmetrically
• about the mirror axis
• Any ray that that passes through the center of
  curvature returns on
• itself

Any two of these rays is sufficient to locate an
image
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Curved Mirrors - Spherical Mirrors
Object located at
Object height is
Image located at
Image height is
The shaded triangles are similar triangles
M is the magnification Image height is negative
if image is inverted
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Curved Mirrors - Spherical Mirrors
Object located at
l
Object height is
Image located at
Image height is
The shaded triangles are similar triangles
Mirror Equation
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Curved Spherical Concave Mirrors
Object located at
Object height is
l
Image located at
Image height is
As it turns out the image may also be virtual.
This occurs when object is closer to the mirror
than the focal length. The image is then upright
and virtual.
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Curved Spherical Convex Mirrors
Object located at
Object height is
Image located at
Image height is
For a Convex mirror the focal length always
satisfies f lt 0. This implies
Image is always virtual, upright, and reduced
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Hubble Mirror
Mirror Equation
A technician stands 3.85m in front of the Hubble
mirror which has a focal length of 5.52m.
(a) The location of the techs image is?
Why is the answer lt0?
The tech is standing inside the focal length. The
image Is virtual!
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Hubble Mirror
Mirror Equation
A technician stands 3.85m in front of the Hubble
mirror which has a focal length of 5.52m.
(b) The magnification of techs image is?
If the technician is 15m in front of the mirror
then
The image is real, reduced, and inverted.
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Do you need a mirror to form an image?Not
necessarily. You can do reasonably well with a
flat refracting surface.

• The image formed by a flat refracting surface is
  on the same side of the surface as the object
• The image is virtual
• The image forms between the object and the
  surface
• The rays bend away from the normal since n1 gt n2

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Depth perception looking into water

• The object is at O, the image is at I
• Assume a light ray from the
• object has an incident angle of
• Assume light ray from the
• Image has an incident angle of

If the depth of a pool is p2m then from Snells
law
The depth of the pool appears to be 1.5m
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Thin Lenses
A thin lens consists of a piece of glass or
plastic, ground so that each of its two
refracting surfaces is a segment of either a
sphere or a plane (a sphere of infinite radius)
A lens is thin when the radii of curvature are
much bigger than its thickness. Lenses have two
major applications light collection and imaging
Diverging lenses are thickest at the edges
and have negative focal lengths
Converging lenses are thickest in the middle
and have positive focal lengths
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Converging lens and its focal length, f
Light collection
The parallel rays pass through the lens and
converge at the focal point. The parallel rays
can come from the left or right of the lens.
A thin lens has two focal points equidistance
from the lens, corresponding to parallel rays
from the left and from the right. A thin lens is
one in which the distance between the surface of
the lens and the center of the lens is negligible
compared to f.
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Diverging lens and its focal length, f
The parallel rays diverge after passing through
the diverging lens. The focal point is the point
where the rays appear to have originated.
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Imaging
f
l

• Three principal rays emanating from every point
  of the object
• A ray parallel to the axis of the lens on the
  front side passes through the focal point on the
  back side.
• A ray that passes through the center of the lens
  and does not get refracted.
• A ray that passes through the focal point on the
  front side emerges parallel to the axis of the
  lens on the back side.

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Ray Diagram for Converging Lens
f
l

• If the object is further away from the lens than
  the front focal point, l gt f, gt the image is
  real, inverted, and located behind the lens

If the object is located at more than 2f, l gt
2f, gt the image is reduced. If the object is
located at f lt l lt 2f, the image is magnified.
WHY?
What is different between a concave mirror and a
converging lens?
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Ray Diagram for Converging Lens
l
f
If the object is closer to the lens than the
front focal point, l lt f, gt the image is
virtual, upright, magnified, and in front of the
lens
The image can only be viewed from behind the lens!
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The situation is pretty much the same no matter
where the object is located.
Ray Diagram for Diverging Lens.
f
l

• The image is virtual, and can only be seen
  through the lens.
• The image is upright and is always reduced in
  size compared with the object.

Note the analogy with convex mirrors!
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Lens Equation
The Lens equation is the same form as the
mirror equation.l and l are both considered
positive for the case shown. Whereas l is
positive in the mirror equation when the image is
in front of the mirror. They become equal, when
l l 2f
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Lens magnification
The two shaded triangles, blue and gold, are
right-angled and similar. Therefore, for the lens
magnification, M, we haveThe - sign is taken
to signify the fact that the image is inverted.
http//www.mtholyoke.edu/mpeterso/classes/phys301
/geomopti/lenses.html