Solitons, Momentum & Wave Fronts in Imaging Science Darryl D. Holm
Figure 26-1 Wave Fronts and Rays
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Transcript of Figure 26-1 Wave Fronts and Rays
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Figure 26-1Wave Fronts and Rays
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Figure 26-2Spherical and Planar Wave Fronts
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Figure 26-3Reflection from a Smooth Surface
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Reflection
• Law of reflection
qi=qr
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Figure 26-4Reflection from Smooth and Rough Surfaces
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Figure 26-6Locating a Mirror Image
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Figure 26-8Spherical Mirrors
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Figure 26-9Concave and Convex Mirrors
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Figure 26-10Parallel Rays on a Convex Mirror
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Figure 26-12Parallel Rays on a Concave Mirror
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Figure 26-13Spherical Aberration and the Parabolic Mirror
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Figure 26-14Principal Rays Used in Ray Tracing for a Concave Mirror
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Figure 26-15Principal Rays Used in Ray Tracing for a Convex Mirror
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Figure 26-17Image Size and Location in a
Convex Mirror
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Figure 26-18Image Formation with a Concave Mirror
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Example 26-3Image Formation
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Mirrors
The mirror equation
0
1 1 1
id d f =
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Mirrors
Magnification
i i
o o
h dmh d
= =
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Mirrors
do =distance of the object from the mirrordi =distance of the image from the mirrorf= focal length of the mirror
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Mirrors
Distances in front of the mirror are positive.Distances behind the mirror are negative.
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Table 26-1Imaging Characteristics of Convex
and Concave Spherical Mirrors
Convex MirrorObject location Image orientation Image size Image type
Arbitrary Upright Reduced Virtual
Concave MirrorObject location Image orientation Image size Image type
Beyond C Inverted Reduced Real
C Inverted Same as object Real
Between F and C Inverted Enlarged Real
Just beyond F Inverted Approaching infinity Real
Just inside F Upright Approaching infinity Virtual
Between mirror and F Upright Enlarged Virtual
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Mirrors
Mirror problems:19, and 21-24 on page 883.Ray tracing worksheet.
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Refraction
When light transitions between two media with different indices of refraction, it will change direction if it transitions at an angle to the demarcation between the two media.
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Refraction
Angles of incidence and angles of refraction are measured in reference to a line normal (perpendicular) to the line of demarcation between media.
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The index of refraction (n) for a medium is defined as the speed of light in vacuum (c) divided by the speed of light in the medium(v).
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cnv
=
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Exercise 26-4Find the angle of refraction
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Refraction
There is a mathematical relationship that is used to calculate the amount of bending called Snell’s Law.
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Refraction
1 1 2 2sin sinn nq q=
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Refraction
If a ray is transitioning from a medium of lesser n to a medium of greater n it will bend toward the normal.
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Refraction
If a ray is transitioning from a medium of greater n to a medium of lesser n it will bend away from the normal.
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Figure 26-24Light Propagating Through a Glass Slab
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Refraction
Problems 37-42 on page 883.
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Lenses
Refractive properties of materials are useful in manipulating light for imaging purposes through the use of lenses.
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Lenses
Lenses consist of two main types converging and diverging.
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Figure 26-29A Variety of Converging and Diverging Lenses
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Figure 26-32The Three Principal Rays
Used for Ray Tracing with Convex Lenses
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Figure 26-33The Three Principal Rays
Used for Ray Tracing with Concave Lenses
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Figure 26-35aRay Tracing for a Convex Lens
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Figure 26-34The Image Formed by a Concave Lens
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Lenses
The lens equation
0
1 1 1
id d f =
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Lenses
Magnification
i i
o o
h dmh d
= =
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Lenses
do =distance of the object from the lensdi =distance of the image from the lensf= focal length of the lens
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LensesFocal lengthf is positive for converging(convex) lenses f is negative for diverging (concave) lensesMagnificationm is positive for upright images (same orientation as the object) m is negative for inverted images (opposite orientation of object)
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LensesImage distancedi is positive for real images (on the opposite side of the lens from the object)di is negative for virtual images (on the same side of the lens from the object)Magnificationm is positive for upright images (same orientation as the object) m is negative for inverted images (opposite orientation of object)
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Lensesdo is positive for real objects (from which light diverges)do is negative for virtual objects (toward which light converges)
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Lenses
Problems 63-67 on page 885.Ray tracing worksheet.
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Dispersion of light
The index of refraction in a substance is different for light of different frequencies.
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Dispersion of light
The greater the frequency, the greater the index of refraction.
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Dispersion of light
Violet light will bend more than red light or green light, and therefore a separation of colors occurs.
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Example 26-8Prismatics
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Figure 26-37Dispersion in a Raindrop
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Figure 26-38How Rainbows Are Produced
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Dispersion of light
Problem 77 on p 885