Ray (Geometric) Optics

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Chapter 7

• Ray (Geometric) Optics

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1. Geometry (???),Optics (??)
2. Reflection (??), refraction (??) penetrate (??)
3. Ultraviolet (???) infrared (???),
4. incident ray (???), reflected ray (???),
   refracted ray (???), paraxial ray (????)
5. dielectrics (???), medium(media,??),
6. Spectrum (??), refractive index (???) ,
7. fibrescope (??), fiber (??) ,
8. interface (??), focus (??,??), focal distance
9. dioptric strength (???), diopter (???)

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We know that visible light occupies only a tiny
portion in the vast electromagnetic spectrum. Of
course, it is a very important part of the
spectrum for human beings, since we detect
visible radiation with our eyes. Moreover, we
distinguish the various visible wavelengths and
frequency by their different colors.
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Light is able to propagate through certain
materials. It can not pass through any metal, but
it can penetrate (??) some dielectrics (???).
When light travel in a transparent medium such
as air or glass, the velocity is always lower
than that in the free space. The ratio of the
free space velocity to the velocity in a medium
is called refractive index (???) of the medium.
Velocity of light in the free space
Velocity of light in a medium
The refractive index depends on the medium in
question and on the wavelength of the light.
(velocity ?f )
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7.1 Reflection and Refraction

• Lights can change their propagating direction at
  the border of a medium or on the boundary between
  two media. Lets see what kind of rules they
  should obey.
• Laws of reflection and refraction

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Medium 1 Refractive index n1
(1) The incident rays (???) (2) reflected ray
(???) (3) refracted ray (???) (4) Three angles
Reflected ray
Incident ray
?3
?1
?2
Medium 2 Refractive index n2
incident angle, reflective angle, and refractive
angle
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Law of reflection Angle of incident Angle
of reflection
Law of refraction
n1 is the refractive index of medium 1 and n2 is
that of medium 2.
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2. Total internal reflection (???)
When light is incident on an interface (??) from
the optically denser medium, it might cause total
internal reflection. At the certain critical
angle of incidence, all of the incident light is
reflected and there are no refraction lights.
This phenomenon is called total internal
reflection. The critical angle can be easily
calculated as the refractive angle in this case
is 90 degree.
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This phenomenon is widely used in modern
technology. For example, light pipe. Light is
introduced into one end of a thin glass fiber
(??) that does not have any sharp bends. As the
light progresses, it strikes the walls of the
fiber at the incident angles that always exceed
the critical angle on the glass-air interface. It
causes the light to follow the pipe of the fiber
just as the electrical current follows the wire
in a circuit. The fiber pipe is widely used in
our daily life ranging from decorative displays
to telephone cables and also in medical treatment
like fibrescope (??).
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7.2 Refraction of a spherical surface and coaxial
spherical system
1. Refraction of a spherical surface
When the boundary (??) of two media (??) is a
spherical surface, light refraction is called
refraction of a spherical surface (????). The
theory of such a refraction is essential and very
important for us to understand the light
phenomenon of eyes and some other optical
systems.
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We consider the paraxial rays (????) only which
agree with
Law of reflection gives
and
From the figure we know
?
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Considering the paraxial rays, we have
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Substituting the relation into
We have
(7.1)
This is the equation of single spherical surface.
It can be applied to all kinds of spherical
surface, such as transparent and reflected
surfaces, concave, convex surfaces.
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Attention (1). Object distance (??) u If the
direction from object to spherical surface is the
same as the direction of light, the object
distance u is positive. Otherwise it is negative.
(??????,??????) (2). Image distance v If the
direction from spherical surface to image is the
same as the direction of light, the image
distance is positive. Otherwise it is negative.
(??????,??????).
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(3). Curvature radius r If the direction from
spherical surface to its center point is the same
as the direction of light, the curvature radius
is positive. Otherwise it is negative.
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2. Definition of focus When the object (??)
distance is infinity, the image (?) distance is
called focal distance and the image point is
called focus.
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The focus of refractive surface.
F1

The first focus of the refractive surface.
f1
The first focal distance
At this situation, u f1, v?8
?
?
?
The first focal distance is
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The second focus of the refractive surface
n1
Axis of the system
n2
In this case, u ? 8, v f2
?
?
The second focal distance is
?
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It is found that f1 and f2 are generally
different. But the relation between them is
related to the refractive indices (???) of the
two medium. It is easy to find that
The ratio of the refractive index to the focal
distance in the medium is called dioptric
strength (???) of the spherical surface, denoted
by D, which is a measure of its ability to cause
a beam to converge.
With units of diopter (???).
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Example 7-1 One end of a cylindrical glass rod is
ground (?) to a hemi-spherical surface of radius
R 20 mm. (1) When the rod is in air, find the
image distance of a point object on the axis of
the rod, 80 mm to the left of the convex (2)
when the rod is immerged in water of index 1.33,
find the image distance. Solution (1) when the
rod is in air, n1 1.0, n2 1.5, r
20mm, u 80 mm. Substituting these known
conditions into the equation of single spherical
surface, we have
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The image is therefore formed at the right of the
vertex and at a distance of 120mm from it. (2)
Now n1 1.33, we have
The fact that v is negative means that the rays,
after refraction by the surface, are not
converging but appear to diverge from a point
180mm to the left of vertex. This kind of image
is called virtual image.