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![Page 1: Homework Notes If you are struggling with the homework, start working on it early enough that you can come to office hours if needed. You can go to the.](https://reader030.fdocuments.net/reader030/viewer/2022032722/56649ce15503460f949abfde/html5/thumbnails/1.jpg)
Homework Notes• If you are struggling with the homework, start
working on it early enough that you can come to office hours if needed.
• You can go to the help room even when one of us is not there, at least for the first half of the course.
• Do not email me Wednesday night with homework questions.
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Chapter 3: Mirrors and Lenses
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Chapter 3: Mirrors and Lenses
• Mirrors– Spherical mirrors– Ray tracing
• Convex mirrors– Image formation– Applications
• Concave mirrors– Image formation– Applications
• Lenses– Refraction– Converging rays– Diverging rays
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Reflection Review• Recall our ray tracing of a flat mirror• Recall that there are “special” rays that are
sufficient for locating the image
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Clicker Question• Which shows the correct location, orientation,
and size for the image?
A)
D) E)
C)B)
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Spherical Mirrors
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What is the normal to a curved surface and how is it used to find rays?
• To find the normal to a curved surface at a point where a ray hits that surface (and will be reflected or refracted)– First draw a tangent line to the curve
(or tangent plane to the surface)– The normal is perpendicular to that
line or plane and going through the point
– Once you have drawn the normal you can draw the reflected or refracted ray
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Ray Tracing & Spherical Mirrors
Radius of Curvature: The radius of the sphere the mirror is “cut from”
Center of Curvature (C): The center of the sphere the mirror is cut from
Focal Point (F): The point where rays from a distance appear to converge
For a spherical mirror, the focal point is halfway between the surface and the center of curvature
Paraxial Ray: A ray coming on to the mirror parallel to the axis
CF
radius of curvature
paraxial rays
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Convex vs. Concave
Convex Concave
• Spherical mirrors are drawn in two dimensions, so you have to imagine the 3D mirror this line represents
• Both convex and concave mirrors obey the same law of reflection, but they make different kinds of images
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Sources of Paraxial Rays
• The rays coming from a distance source can be considered approximately paraxial when they reach a mirror
Convex mirror
• The rays from a nearby source, such as a candle or bare light bulb, cannot be considered paraxial
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Special Rays: Convex Mirror
CFaxis
Ray 1 Rule: All rays incident parallel to the axis are reflected so that they appear to be coming from the focal point, F.
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Special Rays: Convex Mirror
CFaxis
Ray 2 Rule: All rays that (when extended) pass through C are reflected back on themselves
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Special Rays: Convex Mirror
CFaxis
Ray 3 Rule: All rays that (when extended) pass through F are reflected back parallel to the axis.
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Locating an Image: Convex Mirror
CFaxis
Image properties:•virtual (behind the mirror)•right-side up•closer to the mirror than the object•smaller than the object.
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Compare to Flat Mirror
Image properties:•virtual (behind the mirror)•upside down•the same distance from the mirror as the object•the same size as the object
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Clicker Question
• The image formed in a convex mirror is smaller than the object. This would make a convex mirror useful for which application?
A. Makeup or shaving mirrorB. Wide-angle mirror, such as on a car or a blind
intersectionC. A mirror in a clothing store dressing room
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Convex Mirrors
• Because the image is smaller than the object, convex mirrors reflect from wider angles than flat mirrors.
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Concave Mirrors
C Faxis
Ray 1 Rule: All rays incident parallel to the axis are reflected so that they pass through the focal point, F.
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C Faxis
Concave Mirrors
Ray 2 Rule: All rays that pass through C are reflected back on themselves
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Concave Mirrors
C Faxis
Ray 3 Rule: All rays that pass through F are reflected back parallel to the axis.
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Image Formation: Concave Mirrors
C F
Image properties:•real (in front of the mirror)•upside down•farther from the mirror than the object•larger than the object.
Object location: Between the center of curvature and the focal point
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Concave Mirrors
C F
Image properties:•virtual (behind the mirror)•right-side up•farther from the mirror than the object•larger than the object.
Object location: Between the surface and the focal point
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Concave Mirrors
C F
Object location: Past the center of curvature
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Concave Mirrors: Clicker Question
C F
Object location: Past the center of curvature
Is the image
A.Real and magnifiedB.Real and reducedC.Virtual and magnifiedD.Virtual and reduced
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Clicker Question
• The inside of a spoon bowl is a concave surface with a radius of curvature of a couple of inches (depending on the spoon). If you hold it about a foot from your face, what will your face look like?
A. Normal size, upside downB. Normal size, right side upC. Smaller, upside downD.Smaller, right side up
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Concave Mirrors: Application
Because rays coming in parallel, as from a very distant source, are all reflected to the focal point, a receiver placed there will pick up the waves received over the large area of the dish, instead of just the small area of the receiver itself.
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Concave Mirrors: Application• What if we put a light source at the
focal point of a concave mirror?• All the rays emitted by the light go
through the focal point, and are therefore reflected parallel to the axis of the mirror.
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Spherical Lenses
What if we don’t want to have to look at a reflection to magnify or reduce an image?We can use refractive optics instead (lenses)
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Convex Glass Surface
CFaxis
A concave surface is called “converging” because parallel rays converge towards one another
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Convex Glass Surface
C Faxis
The surface is converging for both air to glass rays and glass to air rays
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C Faxis
A concave surface is called “diverging” because parallel rays diverge away from one another
Concave Glass Surface
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CF axis
Again, the surface is diverging for both air to glass rays and glass to air rays
Concave Glass Surface