Lenses

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Lenses
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Refraction in Prisms
If we apply the laws of refraction to two prisms,
the rays bend toward the base, converging light.
Parallel rays, however, do not converge to a
focus, leaving images distorted and unclear.
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Refraction in Prisms (Cont.)
Similarly, inverted prisms cause parallel light
rays to bend toward the base (away from the
center).
Again there is no clear virtual focus, and once
again, images are distorted and unclear.
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Converging and Diverging Lens
If a smooth surface replaces the prisms, a
well-defined focus produces clear images.
Real focus
Virtual focus
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The Focal Length of Lenses
The focal length f is positive for a real focus
(converging) and negative for a virtual focus.
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The Principal Focus
Since light can pass through a lens in either
direction, there are two focal points for each
lens.
The principal focal point F is shown here.
Yellow F is the other one.
Now suppose light moves from right to left
instead . . .
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Types of Converging Lenses
In order for a lens to converge light it must be
thicker near the midpoint to allow more bending.
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Types of Diverging Lenses
In order for a lens to diverge light, it must be
thinner near the midpoint to allow more bending.
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Terms for Image Construction

• The near focal point is the focus F on the same
  side of the lens as the incident light.

• The far focal point is the focus F on the
  opposite side to the incident light.

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Image Construction
Ray 1 A ray parallel to the lens axis passes
through the far focus of a converging lens or
appears to come from the near focus of a
diverging lens.
Ray 1
Ray 1
F
F
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Image Construction
Ray 2 A ray passing through the near focal point
of a converging lens or proceeding toward the far
focal point of a diverging lens is refracted
parallel to the lens axis.
Ray 2
Ray 2
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Image Construction
Ray 3 A ray passing through the center of any
lens continues in a straight line. The refraction
at the first surface is balanced by the
refraction at the second surface.
Ray 3
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Images Tracing Points
Draw an arrow to represent the location of an
object, then draw any two of the rays from the
tip of the arrow. The image is where lines cross.
1. Is the image erect or inverted?
2. Is the image real or virtual?

• Real images are always on the opposite side of
  the lens. Virtual images are on the same side.

3. Is it enlarged, diminished, or same size?
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Object Outside 2F
Real inverted diminished
1. The image is inverted i.e., opposite to the
object orientation.
2. The image is real i.e., formed by actual
light rays in front of mirror.
3. The image is diminished in size i.e., smaller
than the object.
Image is located between F and 2F
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Object at 2F
Real inverted same size
1. The image is inverted i.e., opposite to the
object orientation.
2. The image is real i.e., formed by actual
light rays in front of the mirror.
3. The image is the same size as the object.
Image is located at 2F on other side
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Object Between 2F and F
Real inverted enlarged
1. The image is inverted i.e., opposite to the
object orientation.
2. The image is real formed by actual light rays
on the opposite side
3. The image is enlarged in size i.e., larger
than the object.
Image is located beyond 2F
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Object at Focal Length F
Parallel rays no image formed
When the object is located at the focal length,
the rays of light are parallel. The lines never
cross, and no image is formed.
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Object Inside F
Virtual erect enlarged
1. The image is erect i.e., same orientation as
the object.
2. The image is virtual i.e., formed where light
does NOT go.
3. The image is enlarged in size i.e., larger
than the object.
Image is located on near side of lens
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Review of Image Formations
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Diverging Lens Imaging
All images formed by diverging lenses are erect,
virtual, and diminished. Images get larger as
object approaches.
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Analytical Approach to Imaging
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Same Sign Convention as For Mirrors
1. Object so and image si distances are positive
for real and images negative for virtual images.
2. Image height hi and magnifi-cation M are
positive for erect negative for inverted images.
3. The focal length f and the radius of curvature
R is positive for converging mirrors and negative
for diverging mirrors.
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Example 1. A magnifying glass consists of a
converging lens of focal length 25 cm. A bug is
8 mm long and placed 15 cm from the lens. What
are the nature, size, and location of the image?
so 15 cm f 25 cm
si -37.5 cm
The fact that si is negative means that the image
is virtual (on same side as object).
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Example 1 Cont.) A magnifying glass consists of
a converging lens of focal length 25 cm. A bug
is 8 mm long and placed 15 cm from the lens.
What is the size of the image?
so 15 cm si -37.5 cm
ho
hi
hi 20 mm
The fact that hi is positive means that the image
is erect. It is also larger than object.
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Example 2 What is the magnification of a
diverging lens (f -20 cm) if the object is
located 35 cm from the center of the lens?
First we find si . . . then M
si 12.7 cm
M 0.364
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Example 3 Derive an expression for calculating
the magnification of a lens when the object
distance and focal length are given.
From last equation si -soM
Substituting for si in second equation gives . . .
Thus, . . .
Use this expression to verify answer in Example 4.
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Summary
A converging lens is one that refracts and
converges parallel light to a real focus beyond
the lens. It is thicker near the middle.
A diverging lens is one that refracts and
diverges parallel light which appears to come
from a virtual focus in front of the lens.
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Summary of Math Approach
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Summary of Sign Convention
1. Object so and image si distances are positive
for real and images negative for virtual images.
2. Image height hi and magnifi-cation M are
positive for erect negative for inverted images.
3. The focal length f and the radius of curvature
R is positive for converging mirrors and negative
for diverging mirrors.