Download Mirrors and Reflection NOTES

Mirrors and Reflection
Ray Model of Light
Light travels in straight lines, called rays.
Reflection
The bouncing back of a light ray from a surface.
Law of Reflection
When a light ray is incident upon a reflecting surface, the angle of reflection is
equal to the angle of incidence. Both of these angles are measured relative to a
normal drawn to the surface. The incident ray, the reflected ray, and the normal
all lie in the same plane.
Normal
A perpendicular drawn to a surface.
Angle of Incidence
The angle the incident ray makes with the normal
Angle of Reflection
The angle the reflected ray makes with the normal
Diffuse reflection
When rays are reflected from a rough surface, they are reflected in many
directions and no clear image is formed. None of the normals drawn to the surface
(at the point at which the incident light ray strikes the surface) are parallel.
Regular reflection
When rays are reflected from a smooth surface, they are reflected so that a clear
image is formed. The reflected rays are nearly parallel. The normals drawn to the
surface (at the point at which the incident ray strikes the surface) are nearly
parallel.
An applet explaining the physics of a rainbow. Rainbow
http://www.phy.ntnu.edu.tw/java/Rainbow/rainbow.html
Types of mirrors:
1. Plane mirrors
A flat mirror that reflects light rays in the same order as they approach the mirror.
2.
Concave mirrors
A converging mirror; light rays that strike the mirror surface are reflected so that
they converge, or "come together," at a point
3.
Convex mirrors
A diverging mirror; light rays that strike the mirror surface are reflected so that
they diverge, or "go apart," and they never come to a point.
Type of images:
1. Real images
formed by converging light rays; can be projected on a screen;
orientation=inverted
2. Virtual images
formed by diverging light rays; cannot be projected on a screen; orientation=erect
Characteristics of plane mirror images:
1.
2.
3.
4.
5.
Object size = image size
Object distance = image distance
Orientation = erect
Always forms a virtual image
Image is reversed, left to right
A game to play using a plane mirror. Mirror Game
http://www.phy.ntnu.edu.tw/java/optics/mirrorgame_e.html
Steps for drawing a plane mirror ray diagram:
1. A ray that strikes perpendicular to the mirror surface, reflects perpendicular to the
mirror. This reflected ray is extended behind the mirror
2. A ray that strikes the mirror at any angle reflects so that the angle of incidence
equals the angle of reflection; the reflected ray is extended behind the mirror.
Curved mirror terminology: (a concave mirror is drawn as an example)
center of curvature (C)
the center of the circle of which the mirror represents a small arc
focus (F)
the point where parallel light rays converge; the focus is always found on the
inner part of the "circle" of which the mirror is a small arc; the focus of a mirror is
one-half the radius
vertex (V)
the point where the mirror crosses the principal axis
Principal axis
a line drawn through the vertex, focus, and center of curvature of the mirror upon
which the object rests
focal length (f)
the distance from the focus to the vertex of the mirror; the focal length is one-half
the radius of curvature
radius of curvature
the distance from the center of curvature to the vertex of the mirror; it corresponds
to the radius of the circle
Concave mirror
the reflecting surface of the mirror is on the inside; the object and focus are
located on the same side of the mirror
Characteristics of concave mirrors:
1. The focal length is positive (because the object and the focus are on the
same side of the mirror)
2. The object and the focus are on the same side of the mirror (inside the arc)
3. Real images can be formed by the mirror when the object is outside of the
focus; an inverted image is formed
4. Virtual images are formed by the mirror when the object is within the
focus; an erect image is formed
5. No image is formed when the object is at the focus
6. When the object is at the center of curvature, an inverted image is formed
at the center of curvature
Ray diagrams for concave mirrors:
There are three principal rays. You may locate an image using any two of the
principal rays.
1. A ray incident upon the mirror that is parallel to the principal axis, reflects
through the focus.
2. A ray incident upon the mirror that passes through the focus, reflects
parallel to the principal axis.
3. A ray that connects the top of the object and the center of curvature
reflects back upon itself.
An interactive applet that allows you to create images for both mirror types using
ray diagrams. This is an excellent way to see how each of the three principal rays
for a concave mirror are drawn. You may drawn each individually. You may draw
any two to locate the image. Or, you may locate the image using all three. Ray
Diagrams http://www.physics.nwu.edu/ugrad/vpl/optics/mirrors.html
Mathematical prediction of image location:
where f is the focal length (remember to assign it a sign), do is the object distance,
and di is the image distance
Mathematical prediction of image height:
where hi is the image height, ho is the object height, and di is the image distance,
and do is the object distance
Magnification ratio:
where hi is the image height, ho is the object height, and di is the image distance,
and do is the object distance
Convex mirrors
the reflecting surface is on the outside; the object and the focus are on opposite
sides of the mirror (remember-the focus is on the "inside" of the circle); the object
is located on the outside
Characteristics of convex mirrors:
1. The focal length is negative (because the object and the focus are on
opposite sides of the mirror)
2. The object and the focus are on opposite sides of the mirror (the focus is
on the inside of the mirror and the object is on the outside)
3. Only virtual images are formed; all images are smaller than the object
Ray Diagrams for convex mirrors:
There are three principal rays. You may locate an image using any two of the
principal rays.
1. A ray incident on the mirror that is parallel to the principal axis is reflected
in a line even with the focus (extend the reflected ray behind the mirror so
that it passes through the focus).
2. A ray incident on the mirror that passes through the focus is reflected
parallel to the principal axis (extend the reflected ray behind the mirror
parallel to the principal axis).
3. A ray that connects the top of the object and the center of curvature
reflects back upon itself.
An interactive applet that allows you to create images for both mirror types using
ray diagrams. This is an excellent way to see how each of the three principal rays
for a convex mirror are drawn. You may drawn each individually. You may draw
any two to locate the image. Or, you may locate the image using all three. Ray
Diagrams
http://www.physics.nwu.edu/ugrad/vpl/optics/mirrors.html
What happens to image distance if the surface of the mirror is curved? A plane
mirror produces a virtual image that is the same size as the object. If the mirror is
bent so that it becomes concave, the virtual image distance increases and the
virtual image size becomes larger, relative to the object. If the mirror is bent so
that it becomes convex, the virtual image distance decreases and the virtual image
size becomes smaller, relative to the object.
Summary of Sign Conventions for Spherical Mirrors
Focal Length
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f is positive for a concave mirror. The real side of the mirror is the same
side as the focus.
f is negative for a convex mirror. The virtual side of the mirror is the
opposite side as the focus.
Object Distance
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do is positive for a real object (the object is in front of the mirror)
do is negative for a virtual object (the object is behind the mirror)
Image Distance
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di is positive for a real image (the image is in front of the mirror)
di is negative for a virtual image (the image is behind the mirror)
Magnification
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m is positive for an image whose orientation is the same as the object
m is negative for an image whose orientation is inverted with respect to
the object
Mirrors Applet for AP
http://www.phy.ntnu.edu.tw/java/Lens/lens_e.html
Diverging Mirrors Applet for AP
http://webphysics.ph.msstate.edu/javamirror/ipmj/java/dmirr/index.html
AP Multiple Choice Questions on Mirrors & Reflection
1. Questions deal with the type of image created by a mirror. Which type
forms real images? Which type forms virtual images? When are images
formed by mirrors smaller than the object? The same size as the object?
Larger than the object?
2. They will give you an object in front of a mirror. You must predict the size
and orientation of the image relative to the object. You must predict the
location of the image.
3. Be able to determine the focal length when given the radius of curvature.
4. Know that parallel light rays (those from a very distant object) converge at
the focus.
5. Be able to locate the position of an object formed by a plane mirror. Be
able to predict the image's orientation.
AP Free Response Questions on Mirrors & Reflection
1. There have not been many free response questions involving mirrors in
recent years.
2. In past years, an object was located in front of a mirror (ususally concave).
Be able to use the three principal rays to locate the image when the object
is within the focus and outside of the focus. Be able to predict how any ray
drawn through the top of the object will reflect (apply the law of
reflection).
3. Be able to state whether the image is real or virtual and be able to support
your conclusion.
4. Apply the mirror equation to calculate image distance. Calculate image
height.
5. In recent years, they combine a question on mirrors with a free response
question on lenses. For example, they have a converging lens with an
object located on its left. They add a concave mirror on the right of the
lens and ask you to locate the final image using a ray diagram.
Mirrors and Billiards shows how to use the law of reflection in pool (a pool game
is at the bottom of the page)
http://www.phy.ntnu.edu.tw/java/billiards/billiards.html
Mirrors Sample Problems
Find the image mathematically and using a ray diagram. Find the magnification ratio.
Always use a one cm high object.
1. An object is placed 30 cm in front of a concave mirror with a focal length of 10
cm.
2. An object is placed 10 cm in front of a concave mirror with 12 cm radius of
curvature.
3. An object is placed 5 cm in front of a concave mirror with 10 cm focal lenght.
4. An object is placed 5 cm in front of a convex mirror with 8 cm focal length.
5. An object is placed 3 cm in front of a convex mirror with 5 cm focal length.
Mirrors Homework
Locate the image mathematically for all curved mirrors and using a ray diagram for all
mirrors. Use an object height of one centimeter. Calculate the image distance, the image
height, and the magnification ratio. Describe the image characteristics for each (type of
image, relationship between di and do, relationship between hi and ho, and the image
orientation).
1. Locate the image produced by a plane mirror for a triangle.
2. An object is placed 5 cm in front of a concave mirror with a focal length of 2 cm.
Ans: 3.33 cm, -0.67 cm; -0.67
3. An object is placed 5 cm in front of a concave mirror with a radius of curvature of
5 cm. Ans: 5 cm; -1 cm; -1
4. An object is placed 5 cm in front of a convex mirror with a focal length of 2 cm.
Ans: -1.43 cm; 0.29 cm; 0.29
5. An object is placed 5 cm in front of a convex mirror with a radius of curvature of
5 cm. Ans: -1.67 cm; 0.33 cm; 0.33
AP Physics B - Geometric Optics Objectives
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Students should understand the principles of reflection and refraction so they can:
1. Determine how the speed and wavelength of light change when light
passes from one medium to another.
2. Show on a diagram the directions of reflected and refracted rays.
3. Use Snell's law to relate the directions of the incident ray and the refracted
ray, and teh indices of refraction of the media.
4. Identify conditions under which total internal reflection will occur.
Students should understand image formation by plane or spherical mirrors so they
can:
1. Relate the focal point of a spherical mirror to its center of curvature.
2. Given a diagram of a mirror wiht the focal point shown, locate by ray
tracing the image of a real object and determine whether the image is real
or virtual, upright or inverted, enlarged or reduced in size.
Students should understand image formation by converging or diverging lenses so
they can:
1. Determine whether the focal length of a lens is increased or decreased as a
result of a change in the curvature of its surfaces or in the index of
refraction of the material of which the lens is made or the medium in
which it is immersed.
2. Determine by ray tracing the location of the image of a real object located
inside or outside the focal point of the lens, and state whether the resulting
image is upright or inverted, real or virtual.
3. Use the thin lens equation to relate the object distance, image distance, and
focal length for a lens, and determine the image size in terms of the object
size.
4. Analyze simple situations in which the image formed by one lens serves as
the object for another lens.