Physics 272
April 28
Spring 2015
www.phys.hawaii.edu/~philipvd/pvd_15_spring_272_uhm
go.hawaii.edu/KO
Prof. Philip von Doetinchem
[email protected]
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Geometric Optics
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It is important to understand the difference between
the position of the actual object and the image of the
same object at a different position
Light rays are deflected by refraction or reflection
from objects
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These light rays appear at the image point
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Make use of the ray model and geometry
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Reflection and refraction at a plane surface
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An object radiates light rays
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Self-luminous (e.g., light bulb)
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Light reflection from an object
To see an object: no obstruction between observer
and object
Stereo observation by human eyes:
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Brain reconstructs distance to object from light rays of
the same object at different angles
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Reflection at a plane surface
Reflection
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Refraction
Let's make it easy:
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Assume point-like objects
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Every object can be viewed as the
sum of many different point-like objects
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Smooth surfaces (reflection and
refraction in uncorrelated directions)
Light rays do not actually go through
image point: virtual image
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Image formation by a plane mirror
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Position of virtual image:
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Construct perpendicular reflection from object
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Construct reflection to observer
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Trace both rays virtually through the reflecting surface
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Point of virtual image is at the position where both rays meet
No matter where the observer is located the virtual
image is at the same location
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Image of an extended object: plane mirror
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The virtual image of each point of an extended one-dimensional object can be
constructed as before
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The object and image distance are the same
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The lateral magnification is defined as:
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On a plane mirror the lateral magnification is positive and the virtual image is
erect
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Image of an extended object: plane mirror
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We can follow the same approach for a threedimensional reflection
Common misconception:
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A mirror is actually not flipping left and right. A
mirror is reversing front and back.
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Image of an extended object: plane mirror
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Virtual images of
mirrors can be
used as images
for additional
mirrors
Both mirrors are
creating the image
point on the other
mirror at the same
spot
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Reflection at a spherical surface
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Plane mirror produces image
of same size and the same
distance
A plane mirror can be
treated as a spherical
mirror with very large radius
Important: the observer sees an
object at the image point, but no
light rays go through this point
→ virtual image
For spherical surface reflected light rays can actually go
through the image point (unlike the plane mirror) → real image
Focusing properties of spherical mirrors are, e.g., essential for
photography and telescopes
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Reflection at a spherical surface
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Relationship between angles:
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Image distance:
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Reflection at a spherical surface
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Assume that angle  is small →  is also small:
This object-image relationship does not depend on angles
→ all light rays meet in one point
Object on the same side of center point of mirror is called concave mirror or converging
mirror
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Focal point and focal length
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When the object is very far from the mirror:
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equation is exactly
true for parabolic mirrors
Therefore parabolic mirrors
are preferred in technical
applications (e.g., telescopes)
If object placed at the focal point
→ trace rays in opposite direction
→ image is created at infinity
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Image of an extended object: spherical mirror
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An object placed further away from the mirror surface than the focal point appears inverted and
can appear smaller, larger, equal in size depending on the position and the focal length:
Covering parts of the reflective service with non-reflective coating
does not take parts of the
Source: http://en.wikipedia.org/wiki/Parabolic_mirror
actual image away → it reduces the intensity (less energy is reflected)
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Image of an extended object: spherical mirror
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If an object is placed closer to a concave mirror than
the focal point → image is virtual and magnified
→ example: makeup mirror
Source: http://en.wikipedia.org/wiki/Parabolic_mirror
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Convex mirrors
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For a positive object distance a convex mirror
always forms an erect, virtual, reduced,
reversed image
Virtual image of a convex mirror projects a
larger field of view than a plane mirror
→ Objects in a convex mirror appear smaller
(“Objects in mirror are closer than they
appear”)
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Convex mirrors
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Light falls on a convex mirror → virtual image behind
mirror
Object-image relation is valid as before if we respect the
sign rules:
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Object distance s is positive
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Radius R is negative
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Image distance s' is negative
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General sign rules for the construction
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When the object is on the same side of the
reflecting or refracting surface as the incoming
light, the object distance s is positive; otherwise
negative
When the image is on the same side of the
reflecting or refracting surface as the outgoing light,
the radius of curvature is positive; otherwise it is
negative
When the center of curvature is on the same side as
the outgoing light, the radius of curvature is positive;
otherwise it is negative
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Graphical methods for mirrors
Principal light rays:
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A ray parallel to the axis, after reflection passes through the focal point of a
concave mirror or appears to come from the virtual focal point of a convex mirror
A ray through (or proceeding toward) the focal point is reflected parallel to the axis
A ray along the radius through or away from the center of curvature intersects the
surface normally and is reflected back along its original path
A ray to the vertex is reflected forming equal angles with the axis
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Refraction at a spherical surface
Essential for
understanding
lenses
The same
general laws
for refraction
as for a plane
surfaces apply
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Relationship between angles:
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Refraction law and other conditions:
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Refraction at a spherical surface
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Putting it all together:
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Refraction at a spherical surface
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Object-image relationship for spherical refracting
surface:
Very similar structure compared to the reflection
case, but modified with the index of refraction
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Refraction at a spherical surface
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Magnification:
'
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Snell's law and small angle approximation:
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Thin lenses
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What does thin mean?
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Parallel light rays cross two
spherical surfaces
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Between surfaces material of
different index of refraction
(typically higher)
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After leaving the material:
where do light rays cross the
optic axis?
Surfaces are close to each other
with respect to the length of the lens
→ thin lens: parallel light is focused in focal points
Each side of the lens has one focal point
For a thin lens the focal length on both sides is the same (even for
different radii on both sides)
Contacts or eye glasses are examples of thin lenses
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Thin lenses
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Construction:
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sign rules from the discussion of spherical mirrors
apply to lenses
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Parallel light ray from object is refracted in thin
lens through the focal point on the other side of
the lens
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Light going through the middle of the lens passes
straight through the thin lens (no change in
direction)
For a 3-D object the two directions
perpendicular to the optic axis are reversed,
the arrow along the optic axis is not reversed
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Thin lenses
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Object-image relationship is the same as for
spherical mirrors:
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