Physics 272
April 29
Spring 2014
http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html
Prof. Philip von Doetinchem
philipvd@hawaii.edu
Phys272 - Spring 14 - von Doetinchem - 411
Summary
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Object image relationship:
Phys272 - Spring 14 - von Doetinchem - 412
Summary
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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
Phys272 - Spring 14 - von Doetinchem - 413
Refraction at a spherical surface
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After reflection on a spherical surface → refraction
on a spherical surface
Essential for understanding lenses
The same general laws for refraction as for a plane
surfaces apply
Phys272 - Spring 14 - von Doetinchem - 420
Refraction at a spherical surface
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Relationship between angles:
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Refraction law and other conditions:
Phys272 - Spring 14 - von Doetinchem - 421
Refraction at a spherical surface
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Putting it all together:
Phys272 - Spring 14 - von Doetinchem - 422
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
Phys272 - Spring 14 - von Doetinchem - 423
Refraction at a spherical surface
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Magnification:
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Snell's law and small angle approximation:
Phys272 - Spring 14 - von Doetinchem - 424
Refraction at a spherical surface
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Sign rule add-on:
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Radius is positive if the center of the curvature is on the
outgoing side of the surface and negative if the center is
on the other side.
Phys272 - Spring 14 - von Doetinchem - 425
Refraction at a spherical surface
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Example: water droplets on plants act as spherical
refraction surfaces
→ sunlight is more concentrated
→ plants feel a higher intensity
Plane refracting surface:
magnification is always 1 → does not depend on
index of refraction, image is erect
Phys272 - Spring 14 - von Doetinchem - 426
Image formation by refraction
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Small image in front of a cylindrical glass rod:
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image is inverted and reduced in size
Phys272 - Spring 14 - von Doetinchem - 427
Image formation by refraction
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Immerse glass rod in water (n=1.33):
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the refracted rays do not converge
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and appear to diverge from a point 21.3cm to the
left from the vertex
The result is a virtual image
Image is still erect and the virtual image appears
magnified
Phys272 - Spring 14 - von Doetinchem - 428
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
Contacts or eye glasses are examples of thin lenses
Phys272 - Spring 14 - von Doetinchem - 429
Thin lenses
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Beams of parallel light pass through the lens and
converge in the focal point
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)
Phys272 - Spring 14 - von Doetinchem - 430
Thin lenses
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Construction:
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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)
Phys272 - Spring 14 - von Doetinchem - 431
Thin lenses
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Object-image relationship is the same as for
spherical mirrors:
Phys272 - Spring 14 - von Doetinchem - 432
Thin lenses
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sign rules from the discussion of spherical mirrors
apply to lenses
For a 3-D object the two directions perpendicular to
the optic axis are reversed, the arrow along the
optic axis is not reversed
Phys272 - Spring 14 - von Doetinchem - 433
Diverging lenses
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Converging lens: thicker in the center than at the
edges
Diverging lens: thicker at the edges than at the
center
Parallel rays are diverged → virtual image in focal
point
Phys272 - Spring 14 - von Doetinchem - 434
The Lensmaker's equation
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The image of the first refracting surface is used as
the object position for the second refracting surface
The sketch shows a distance of d between the two
spherical mirrors → we will set distance to zero
Phys272 - Spring 14 - von Doetinchem - 435
The Lensmaker's equation
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Image position after the first surface:
Image of first surface acts as object for second surface. In coming light on second
surface is on the opposite side as the image from surface 1: s2=-s1'
Phys272 - Spring 14 - von Doetinchem - 436
The Lensmaker's equation
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Combining both equations:
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For a lens in air (s1→s, s'2→s', nb = n)
Phys272 - Spring 14 - von Doetinchem - 437
The Lensmaker's equation
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Focal length on both sides of the object are the
same (set object distance and image distance to
infinity):
Be careful: rays at larger distance from optic axis
are not going to the same focus point → abberation
Phys272 - Spring 14 - von Doetinchem - 438
Object position and focal point for a converging lens
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Object further away than focal point:
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Object inside focal point:
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light rays converge and form a real image on the other
side of the lens
Light rays diverge and the image is virtual and larger
than the object
Photography: having the sensor at the right focal
point is essential for a sharp image
Phys272 - Spring 14 - von Doetinchem - 439