Physics 272
April 24
Spring 2014
http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html
Prof. Philip von Doetinchem
[email protected]
Phys272 - Spring 14 - von Doetinchem - 386
Summary
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Light is an electromagnetic wave with particle
properties
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Emitted by accelerated charges
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Wave fronts travel a definite propagation speed
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A light is a line along the direction of propagation
Wavelength and velocity changes (not frequency)
when light is going from one medium to another
Light can be reflected from surfaces
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Incident and reflected angle are identical
Light can also be refracted
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Refracted angle is different to incident angle and depends
on indexes of refraction of the two joining materials
Phys272 - Spring 14 - von Doetinchem - 387
Summary
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Light can be totally reflected if it travels from one
medium with larger n to a lower n medium
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Starting from a certain angle refraction is not longer
possible
Light is typically a superposition of all different types
of electric field and magnetic field directions
(pairwise perpendicular, transverse to propagation
direction)
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Light can be linearly polarized with filters allowing only
one E/B direction to continue
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Circular polarization can also occur if phase angles
between superposing electromagnetic waves are created
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Reflection is a typical mechanism for polarization
Phys272 - Spring 14 - von Doetinchem - 388
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
Phys272 - Spring 14 - von Doetinchem - 389
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
Phys272 - Spring 14 - von Doetinchem - 390
Reflection at a plane surface
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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
Phys272 - Spring 14 - von Doetinchem - 391
Refraction at a plane surface
Objects under water
appear closer to the
surface
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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
Phys272 - Spring 14 - von Doetinchem - 392
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
Phys272 - Spring 14 - von Doetinchem - 393
General sign rules for the construction
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When 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 one 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
Phys272 - Spring 14 - von Doetinchem - 394
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
Phys272 - Spring 14 - von Doetinchem - 395
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.
Phys272 - Spring 14 - von Doetinchem - 396
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
Phys272 - Spring 14 - von Doetinchem - 397
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
Phys272 - Spring 14 - von Doetinchem - 398
Reflection at a spherical surface
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Reflection at a spherical mirror (with center on the
same side as the object)
All reflected light rays 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
Phys272 - Spring 14 - von Doetinchem - 399
Reflection at a spherical surface
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Relationship between angles:
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Image distance:
Phys272 - Spring 14 - von Doetinchem - 400
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
Phys272 - Spring 14 - von Doetinchem - 401
Focal point and focal length
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When the object is very far from the mirror:
If object placed at the focal point
→ trace rays in opposite direction
→ image is created at infinity
Phys272 - Spring 14 - von Doetinchem - 402
Focal point and focal length
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We made a few assumptions for spherical mirrors to
get to the object-image relationship
This equation is exactly
true for parabolic mirrors
Therefore parabolic mirrors
are preferred in technical
applications
(e.g., telescopes)
Source: http://en.wikipedia.org/wiki/Parabolic_mirror
Phys272 - Spring 14 - von Doetinchem - 403
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:
Source: http://en.wikipedia.org/wiki/Parabolic_mirror
Phys272 - Spring 14 - von Doetinchem - 404
Image of an extended object: spherical mirror
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Covering parts of the reflective service with non-reflective
coating does not take parts of the actual image away
→ it reduces the intensity (less energy is reflected)
→ larger mirrors increase the intensity
(important to see faint stars)
Source: http://en.wikipedia.org/wiki/Parabolic_mirror
Phys272 - Spring 14 - von Doetinchem - 405
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
Phys272 - Spring 14 - von Doetinchem - 406
Image formation by a concave mirror
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Mirror radius and focal length:
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Magnification:
Source: http://en.wikipedia.org/wiki/Parabolic_mirror
Phys272 - Spring 14 - von Doetinchem - 407
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
Phys272 - Spring 14 - von Doetinchem - 408
Convex mirrors
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For 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”)
Phys272 - Spring 14 - von Doetinchem - 409
Graphical methods for mirrors
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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
Phys272 - Spring 14 - von Doetinchem - 410