Exam 2 Statistics
Announcements
• HW set 10 due Friday; covers material from Section 23.624.4
• We are skipping section 23.7: “Lens and Mirror
Aberrations”
Average: 10.6
St. Dev.:
High: 19
Low: 3.1
• Grades for Exam 2 are posted on E-learning
• Office hours:
•Tea and cookies with Prof. Kumar; 5 pm today
•My office hours 1-2 today and Thursday
Review:
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Converging lenses
Ray Diagrams for Mirrors
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Choose 3 rays
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Thin Lenses
Ray 1 – parallel to the principle axis;
Ray 2 - through the focal point
Ray 3 - through the center of curvature
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Concave mirrors – image characteristics
depends on object location with respect
to focal length
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Images formed by refraction
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Lenses are transparent; image forms
on opposite side
Image magnification
M =
„
„
„
„
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Atmospheric refraction
positive focal lengths
thickest in the middle
have positive focal lengths
Diverging lenses
diverging lenses
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refracting surfaces are either
spherical or planar
distance between the surface of the
lens and the center of the lens is
negligible
converging lenses
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nq
h'
=− 1
h
n2 p
Sign conventions for lenses
Thin lens - consists of a piece of
glass or plastic
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negative focal lengths
thickest at the edges
have negative focal lengths
1
Focal Length of Lenses
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focal length, ƒ -image distance that
corresponds to an infinite object distance
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same as mirrors
thin lens has two focal points, corresponding to
parallel rays from the left and from the right
Converging lenses
Lens Equations
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DEMO
The geometric derivation of the
equations is very similar to that of
mirrors
M =
Diverging lenses
h'
q
=−
h
p
1 1 1
+ =
p q f
ƒThe equations can be used for both converging and
diverging lenses
ƒ converging lens has a positive focal length
ƒ diverging lens has a negative focal length
Focal Length for a Lens
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Ray Diagram for Converging Lens, p > f
The focal length of a lens is related to the curvature of its
front and back surfaces and the index of refraction of the
material
⎛1
1
1 ⎞
= (n − 1) ⎜
−
⎟
f
⎝ R1 R2 ⎠
the lens maker’s equation
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The image is real
The image is inverted
2
Ray Diagram for Diverging Lens
Ray Diagram for Converging Lens, p < f
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The image is virtual
The image is upright
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How to handle combinations of thin
lenses
Ray Diagrams for Thin Lenses
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As with mirrors, use 3 rays:
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„
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Ray 1 - parallel to the first principle axis and
then passes through (or appears to come from)
one of the focal lengths
Ray 2 - through the center of the lens and
continues in a straight line
Ray 3 - drawn from the other focal point and
emerges from the lens parallel to the principle
axis
There are an infinite number of rays, these
are the obvious ones to use
The image is virtual
The image is upright
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Step 1: image produced by the first lens is calculated as
though the second lens were not present
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Step 2: The image of the first lens is treated as the
object of the second lens!!
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If the image formed by the first lens lies on the back side
of the second lens, then the image is treated at a virtual
object for the second lens
p will be negative
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Step 3: image formed by the second lens is the final
image of the system
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Step 4: The overall magnification is the product of the
magnification of the separate lenses
3
Combination of thin lenses,
example problem
f1 = 10 cm
f2 = 20 cm
p1 = 30 cm
q2 = ??
4