Chapter 36 Image formation

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Chapter 36 Image formation December 1, 3
Mirrors 36.1 Image formed by flat mirrors
Image If a cone of rays from a point object O
arrive at the certain point I, I is called the
image of O. Object distance The distance from
the object to the mirror or lens. p Image
distance The distance from the image to the
mirror or lens. q
Real and virtual images Images are always
located by extending diverging rays back to a
point at which they intersect. A real image is
formed when light rays converge to and diverge
from the image point. Can be displayed on a
screen. A virtual image is formed when light
rays do not converge to the image point but only
appear to diverge from that point. Cannot be
displayed on a screen.
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Geometry can be used to determine the properties
of an image. Two rays are needed to determine the
location of an image. Lateral magnification

• Image formed by a flat mirror
• p q.
• M 1 (h h' ).
• The image is virtual.
• The image is upright.
• The image has a front-back reversal (?inversion
  in handedness).

Example 36.1 Multiple images Question
Handedness of I3.
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36.2 Image formed by spherical mirrors

• Spherical mirror
• Concave mirror
• Convex mirror
• Radius of curvature R
• Center of curvature C
• Center of the spherical segment V
• Principal axis (C---V)
• Paraxial rays Rays that make a small angle with
  the principal axis.

Geometry shows
Mirror equation
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Focal point The image point when p ? ?.
F Focal length The image distance when p ? ?. f
Spherical mirror
The focal point of a spherical mirror dependents
only on its curvature. It does not depend on the
material of the mirror.
Sign conventions and mirror equation (and other
equations) apply to both concave and convex
mirrors.
Different from other texts.
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Ray diagrams are used to determine the position
and size of an image.
Concave mirrors Three key rays are used to
locate an image point Ray 1 Goes parallel to
the principal axis and is reflected through the
focal point. Ray 2 Goes through the focal point
and is reflected parallel to the principal
axis. Ray 3 Goes through the center of curvature
and is reflected back on itself.
This image is real, inverted, minified.
This image is virtual, upright, magnified.
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Convex mirrors Three key rays are used to locate
an image point Ray 1 Goes parallel to the
principal axis and is reflected away from the
focal point. Ray 2 Goes toward the focal point
and is reflected parallel to the principal
axis. Ray 3 Goes through the center of curvature
on the back side and is reflected back on itself.
This image is virtual, upright, minified.
Summary I) Concave mirror, the image can be
real or virtual. i) p gt R/2, the image
is real, inverted. ii) p R/2, the image is
infinitely far. iii) P lt R/2, the image is
virtual, upright. II) Convex mirror, the image
is virtual and upright.
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Read Ch36 1-2 Homework Ch36 (1-19)
3,7,9,17 Due December 12
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December 5 Image formed by refraction 36.3 Image
formed by refraction
Paraxial rays leaving O are refracted at the
spherical surface and focus at the image point I
(Paraxial rays)
Relationship between object and image distances
for a spherical refracting surface.
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Flat refracting surfaces
The image formed by a flat refracting surface is
virtual and is on the same side of the surface as
the object.
Example 36.6
Example 36.7
Quiz 36.4, 36.5
Question 1 What happens to a chopstick inserted
in water? How is it bent? Is it curved? Question
2 What does the chopstick look like in the eyes
of a fish?
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Read Ch36 3-4 Homework Ch36 (20-26)
21,23,26 Due December 12
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Question Can Ursula image everything outside
into her magic ball by refraction?
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December 8,10 Thin lenses
36.4 Thin lenses
Principle of a lens Light passing through a lens
is refracted at two surfaces. The image formed by
the first surface serves as the object for the
second surface.
Description of a lens Index of refraction n,
radii of curvature R1 and R2, and thickness t.
Focal length of a lens the image distance when
object distance is infinite ? Lens makers
equation (thin lens equation)
? Thin lens equation
the same as for a mirror
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Each lens has two focal points, but only one
focal length
Focal length of a diverging lens
Lateral magnification of a lens

• M gt 0, the image is upright and on the same side
  as the object.
• Mlt0, the image is inverted and on the opposite
  side of the object.

Converging lenses Positive focal lengths,
thicker in the middle.
Diverging lenses Negative focal lengths, thicker
at the edges.
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Ray diagrams for a thin converging lens Ray 1
Goes parallel to the principal axis and passes
through the focal point. Ray 2 Goes through the
center of the lens and continues in a straight
line. Ray 3 Goes through the focal point (or
comes from the focal point) and emerges parallel
to the principal axis.
This image is real, inverted, on the back side.
This image is virtual, upright, magnified, on the
front side.
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Ray diagrams for a thin diverging lens Ray 1
Goes parallel to the principal axis and emerges
away from the front focal point. Ray 2 Goes
through the center of the lens and continues in a
straight line. Ray 3 Goes toward the back focal
point and emerges parallel to the principal axis.
This image is virtual, upright, minified, on the
front side.
Example 36.8, 36.9

• Summary
• Converging lens
• i) p gt , the image is real and inverted.
• ii) p lt , the image is virtual and
  upright.
• Diverging lens
• The image is always virtual and upright.

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Combinations of thin lenses
Principle Treat the image formed by the first
lens as the object of the second lens. Note 1)
If the image formed by the first lens lies on the
back side of the second lens, then the image is
treated as a virtual object ( p lt 0) for the
second lens. 2) Overall magnification M
M1M2. Special case two lenses in contact
Example 36.10
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Read Ch36 4 Homework Ch36 (27-39)
28,29,33,36 Due December 15