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3/23/11
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QUESTIONS? PLEASE ASK!
Chapter 23
Mirrors and Lenses
LIGO mirror
Credit: LIGO Laboratory, Caltech
James Webb Space Telescope
Credit: NASA
LIGO mirror
Credit: LIGO Laboratory, Caltech
http://www.ubergizmo.com/15/archives/2010/ 09/diy_macro_lens_for_your_nexus_one.html
Images and Mirrors n Definitions
n object distance p - distance from the object to the mirror, lens
n image distance q - distance from the image to the mirror, lens
n lateral magnification M - ratio of the image height to the object height
n Images are formed at the point where
n The rays of light actually intersect (‘real image’)
n The rays of light appear to originate (‘virtual image’)
n To find where an image is formed, it is always necessary to follow at least two rays of light as they reflect from the mirror
Types of Images for Mirrors and Lenses
n A real image is one in which light actually passes through the image point n Real images can be
displayed on screens
n A virtual image is one in which the light does not pass through the image point n The light appears to
diverge from that point n Virtual images cannot be
displayed on screens n When you look in a flat
mirror, you see a virtual image
Real Image
Virtual Image
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Magnification
n The lateral magnification is defined as
n Magnification doesn’t always mean enlargement n The image can be smaller than the
object (sometimes called de-magnification)
image height h'Mobject height h
= =
Flat Mirrors n One ray starts at P, follows
path PQ and reflects back on itself
n A second ray follows path PR and reflects according to the Law of Reflection
n Both rays appear to come from a single point behind the mirror
n The image is as far behind the mirror as the object is in front n p = |q|
n The image is unmagnified n The image height is the same
as the object height n h’ = h and M = 1
§ The image … § … is virtual § … is upright
§ … has the same orientation as the object
§ There is an apparent left-right reversal in the image
Concave Spherical Mirrors n A spherical mirror has the
shape of a segment of a sphere
n concave spherical mirror - mirror surface on the inner (concave) side of the curve n The mirror has a radius
of curvature of R n center of curvature is the
point C n Point V is the center of
the spherical segment
n A line drawn from C to V is called the principle axis of the mirror
§ Geometry can be used to determine the magnification of the image
§ h’ is negative when the image is inverted with respect to the object
Concave Mirror, Image
n A point source of light placed at O n Rays drawn from O; after reflecting
from the mirror, rays converge at point I
n Point I is called the image point n Light actually passes through the point
so the image is real
M =h 'h
= !qp
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Image Formed by a Concave Mirror
n Relationship between image and object distances
n mirror equation n If an object is very far
away, then p=∞ and 1/p = 0 n Incoming rays are essentially
parallel n In this special case, the image
point is called the focal point
1p+1q=2R
Focal Point and Focal Length, cont
n The distance from the mirror to the focal point is called the focal length n The focal length is ½ the radius of curvature
n The focal point is dependent solely on the curvature of the mirror, not by the location of the object f = R / 2
n The mirror equation can be expressed as
1p+1q=1f
Problem 23.47, p 787 n An object placed 10.0 cm from a
concave spherical mirror produces a real image 8.00 cm away from the mirror. If the object is moved to a new position 20.0 cm from the mirror, what is the position of the image? Is the final image real or virtual?
Convex Mirrors n Rays from any point on the object diverge after reflection as
though they were coming from a point behind the mirror
n Image is virtual - lies behind the mirror at the point where the reflected rays appear to originate
n In general, the image formed by a convex mirror is upright, virtual, and smaller than the object
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Sign Conventions for Mirrors Ray Diagram for Concave Mirror, p > R
n The object is outside the center of curvature of the mirror
n The image is real n The image is inverted n The image is smaller than the object
Ray Diagram for a Concave Mirror, p < f
n The object is between the mirror and the focal point
n The image is virtual n The image is upright n The image is larger than the object
Ray Diagram for a Convex Mirror
n The object is in front of a convex mirror n The image is virtual n The image is upright n The image is smaller than the object
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Images Formed by Refraction n Rays originate from the
object point, O, and pass through the image point, I
n When n2 > n1,
n Real images are formed on the side opposite from the object
M =h 'h
= !n1qn2p
Flat Refracting Surface
n The image formed by a flat refracting surface is on the same side of the surface as the object n The image is virtual n The image forms
between the object and the surface
n The rays bend away from the normal since n1 > n2
Atmospheric Refraction and Mirages n A mirage can be observed
when the air above the ground is warmer than the air at higher elevations
n The rays in path B are directed toward the ground and then bent by refraction
n Related to total internal reflection – n is smaller near the ground
n The observer sees both an
upright and an inverted image
Answer to 23.47