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Geometric Optics
Chapter 34
1Physics 72 Bareza AY 15-16 1st sem
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Chapter 34Geometric Optics
34-1 Reflection and Refraction at a Plane Surface
34-2 Reflection at a Spherical Surface
34-3 Refraction at a Spherical Surface
34-4 Thin Lens
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Reflection and Refraction at a Plane Surface34-1
OBJECTIVES
Given an object in front of a plane mirror:Calculate the location of the image
Calculate the lateral magnification of the image
Determine whether the image will be real or virtual, and uprightor inverted
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Reflection and Refraction at a Plane Surface34-1
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What is an object?anything from which light rays radiate
light could be emitted by the
object itself
light could be emitted by another
source and then reflected from theobject
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Reflection and Refraction at a Plane Surface34-1
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1. Point Object no physical extent
2. Extended Object real object with length, width and height
Point object Pmade up of a very largenumber ofpoint objects
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Reflection and Refraction at a Plane Surface34-1
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What is an image? from which outgoing rays diverge
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An image can be:
1. Real image outgoing rays really do pass through an image point
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An image can be:
2. Virtual image outgoing rays don't actually pass through the image point
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Reflection and Refraction at a Plane Surface34-1
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1. Sign rule for the
object distance s
When the object is on thesame side of the reflecting or
refracting surface as the
incoming light, the object
distance sis positive;
otherwise, it is negative.
Sign Rules
sis positive.
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Reflection and Refraction at a Plane Surface34-1
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2. Sign rule for the
image distance s
When the image is on thesame side of the reflecting or
refracting surface as the
outgoing light, the image
distance s' is positive;
otherwise, it is negative.
Sign Rules
s is negative.
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Reflection and Refraction at a Plane Surface34-1
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3. Sign rule for the
radius of curvature R
of a spherical surface: When the center of curvature C is
on the same side as the
outgoing light, the radius of
curvature is positive; otherwise,
it is negative.
Sign Rules
For a plane reflecting or refracting
surface, Ris infinite.
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Reflection and Refraction at a Plane Surface34-1
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Plane Mirror: Image of a Point ObjectReflection
Note: s is negative
image is virtual
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Reflection and Refraction at a Plane Surface34-1
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Plane Mirror: Image of an Extended ObjectReflection
where: y : object height
y : image height
s : object distance
s: image distance
The image formed by a plane mirror is always erect (y > 0).
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Reflection and Refraction at a Plane Surface34-1
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Lateral Magnification
where: y : object height
y : image height s : object distance
s : image distance
If m > 0: image orientation same with that of object
If m< 0: image orientation different from that of object
If y > 0: image uprightIf y < 0: image inverted
If s > 0: image real
If s < 0: image virtual
Sign Conventions:
If |m| > 1: magnified
If |m| < 1: reduced
If |m| = 1: same size
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Reflection and Refraction at a Plane Surface34-1
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where: y : object height
y : image height
s : object distance
s : image distance
Plane MirrorReflection
Lateral Magnification
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Reflection and Refraction at a Plane Surface34-1
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Example:
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Reflection and Refraction at a Plane Surface34-1
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Example:
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Reflection and Refraction at a Plane Surface34-1
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Seatwork:A bug at about eye level is 5 cm in front of a plane mirror. You
are behind the bug, 20 cm from the mirror. What is the
distance between your eyes and the apparent position ofthe bugs image in the mirror?
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Chapter 34Geometric Optics
34-1 Reflection and Refraction at a Plane Surface
34-2 Reflection at a Spherical Surface
34-3 Refraction at a Spherical Surface34-4 Thin Lens
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Reflection at a Spherical Surface34-2
OBJECTIVES
Given an object in front of a spherical mirror:
Calculate the location of the imageCalculate the lateral magnification of the image
Determine whether the image will be real or virtual, and uprightor inverted
Given an object placed in front of a spherical mirror, drawthe principal rays and locate the image
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Reflection at a Spherical Surface34-2
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Convex Mirror Concave Mirror
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Reflection at a Spherical Surface34-2
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Concave Mirror:Point object
C R> 0
Voptic axis Object P
Image P
s > 0
s> 0
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Reflection at a Spherical Surface34-2
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Concave Mirror:Extended object
C
R> 0
Vy > 0
Object
Image
s > 0
y< 0
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Reflection at a Spherical Surface34-2
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Concave Mirror:Focal Point and Focal Length
where: f > 0: focal length
R > 0: radius of curvature
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Reflection at a Spherical Surface34-2
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Concave Mirror:Focal Point and Focal Length
where: f > 0: focal length
R > 0: radius of curvature
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Reflection at a Spherical Surface34-2
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Concave Mirror:Graphical Method
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Reflection at a Spherical Surface34-2
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Example:
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Reflection at a Spherical Surface34-2
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Seatwork:A mosquito landed 20 cm in front of a concave mirrorwith
20 cm radius of curvature. How far from the mirror will the
mosquitos image be formed?
A. 40 cm behind the mirror
B. 10 cm behind the mirror
C. 10 cm in front of the mirror
D. 20 cm in front of the mirror
E. At infinity
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Reflection at a Spherical Surface34-2
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Convex Mirror Concave Mirror
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Reflection at a Spherical Surface34-2
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Convex Mirror:Point object
CR< 0V
optic axis
Object P
Image P
s > 0
s< 0
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Reflection at a Spherical Surface34-2
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Convex Mirror:Extended object
C
R< 0
V
y > 0
Object
Image
s > 0
y > 0
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Reflection at a Spherical Surface34-2
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Convex Mirror:Focal Point and Focal Length
where: f < 0: focal length
R < 0: radius of curvature
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Reflection at a Spherical Surface34-2
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Convex Mirror:Focal Point and Focal Length
where: f < 0: focal length
R < 0: radius of curvature
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Reflection at a Spherical Surface34-2
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Convex Mirror:Graphical Method
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Reflection at a Spherical Surface34-2
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Example:
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Reflection at a Spherical Surface34-2
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Seatwork:You hold a large silver spoon a distance of 5.0 cm in front of
your face. The radius of curvature of the spoon is -20.0 cm.
What is the distance between the object and the image andthe nature (real or virtual) of the image?
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Chapter 34Geometric Optics
34-1 Reflection and Refraction at a Plane Surface
34-2 Reflection at a Spherical Surface
34-3 Refraction at a Spherical Surface34-4 Thin Lens
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Refraction at a Spherical Surface34-3
OBJECTIVES
Given an object in front of a spherical surface or interfaceseparating two media:Calculate the location of the image
Calculate the lateral magnification of the image
Determine whether the image will be real or virtual, and uprightor inverted
Calculate the apparent depth of an object when observedacross a boundary changing indices of refraction
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Refraction at a Spherical Surface34-3
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Image of a Point Object
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Refraction at a Spherical Surface34-3
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Image of an Extended Object
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Refraction at a Spherical Surface34-3
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Refracting surface:Object-Image Relationship and Magnification
valid for both concave and
convex refracting surface
Note:na : index of refraction of material 1nb : index of refraction of material 2
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Refraction at a Spherical Surface34-3
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Example:
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Refraction at a Spherical Surface34-3
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Seatwork:
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Refraction at a Spherical Surface34-3
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A special case:Plane refracting surface
Object-Image Relationship
Magnification
Radius of Curvature
na nbMaterial 1 Material 2
Plane refracting surface
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Refraction at a Spherical Surface34-3
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Example:
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Refraction at a Spherical Surface34-3
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Seatwork:
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Chapter 34Geometric Optics
34-1 Reflection and Refraction at a Plane Surface
34-2 Reflection at a Spherical Surface
34-3 Refraction at a Spherical Surface34-4 Thin Lens
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Thin Lens34-4
OBJECTIVES
Differentiate a converging lens from a diverging lens
Given an object in front of a lens or series of lenses:Calculate the location of the image
Calculate the lateral magnification of the image
Determine whether the image will be real or virtual, and uprightor inverted
Relate the radii of curvature of the lens in air and its index
of refraction of the focal length of the lens Given an object placed in front of a lens or series of lenses,
draw the principal rays and locate the image
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Thin Lens34-4
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What is a lens?an optical system with two refracting surfaces
Thin lens two spherical surfaces close enough together negligible thickness
Converging Lens
Diverging Lens
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Thin Lens34-4
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Converging Lens thicker at its center than at its edges
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Properties of a Converging Lens
f: focal length (f> 0)
F1 :1st focal point
F2 : 2nd focal point
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Thin Lens34-4
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Converging Lens:Graphical Method and Principal Rays
s> 0s > 0
f > 0
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Thin Lens34-4
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Converging Lenses:Object-image relationship and Magnification
where: f : focal length
s : object distance
s : image distance
If s > 0: image real
If s < 0: image virtual
f> 0 : converging lens
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Thin Lens34-4
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Diverging Lens thicker at its edges than at its center
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Properties of a Diverging Lens
f: focal length (f< 0)
F1 :1st focal point
F2 : 2nd focal point
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Thin Lens34-4
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Diverging Lens:Graphical Method and Principal Rays
s< 0
s > 0
f < 0
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Thin Lens34-4
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Diverging Lenses:Object-image relationship and Magnification
where: f : focal length
s : object distance
s : image distance
If s > 0: image real
If s < 0: image virtual
f< 0 : diverging lens
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Example:
hi34 4
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Example:
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Example:
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Thin Lens34-4
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Diverging lens: f< 0
|f | = 48 cm |f | = 48 cm
s = 16 cm
s = -12 cm
y y'
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Example:
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Lensmakers equation
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Lensmakers equation
where: f : focal length n : index of refraction of thin lens
R1 : radius of curvature of 1st surface
R2 : radius of curvature of 2nd surface
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Thin Lens34-4
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Geometric Optics
End of Chapter 34