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