With
Curved
Mirrors
Created by Derek J. Wells. Under the expressed written consent of Derek J. Wells in
accordance with the rules and by-laws of Derek J. Wells. All events depicted here are
fictional. Any similarity to real life situations are merely coincidental.
Types of Mirrors
The everyday flat type of mirror is called a “plane mirror”. All light travelling
straight towards this mirror reflects right back at you. As such, you always get an
image that is an exact duplicate of you. Remember, MIRRORS REFLECT LIGHT, so
it bounces off them. This may seem silly in that we already know that, but as we
talk of more optical instruments its something you should keep in mind.
Curved mirrors are not flat and therefore light reflects differently off them
making different types of images. There are two types of curved mirrors
A concave mirror.
And
This mirror has a
concave shape when
looking at it from
the left side.
This mirror looks like a
“cave” if you were
walking into it from the
left side.
A convex mirror
This mirror has a
convex shape when
looking at it from
the left side
The concave mirror is also called a converging mirror because it causes horizontal light
rays to converge (come together) when they reflect off the mirror
The convex mirror is also called a diverging mirror because it causes horizontal
light rays to diverge (move apart) when they reflect off the mirror
Terminology
Curved mirrors are approximated to
have a circular shape.
We can make a curved mirror by cutting part of
mirrored circle out.
The mirror was cut
from a circle.
Terminology
The center of the circle that the
mirror is part of is point C.
Point C is called:
C= Center of Curvature
C
R
The radius of the circle
that the mirror is part of is
distance R
Distance R is called:
R= Radius of Curvature
Terminology
C
Principle Axis = The horizontal
line drawn through the center
f
f
f = Focal point (of a concave mirror)
= the point through which all
horizontal rays hitting the mirror
pass through when they reflect
f = Focal point (of convex mirror)
= the point at which all horizontal
rays hitting the mirror appear to
come from when they reflect
IMPORTANT
These focal points are negative (-)
In the convex mirror
The focal point(f) is 1/2 of the distance to the center of curvature point (C)
f=R/2
C
Terminology
Distance object is
placed from the mirror
Also
ho = object height
d0
hi = image height
An object
placed
near a
mirror
C
f
f
C
di
Front Side of Mirror
(the real side)
When images are formed on the
front side of the mirror they are
real images. Real images can be
projected onto a screen.
The image of
the object that
is produced by
the mirror
Distance image
is formed from
the mirror
Back Side of Mirror
(the virtual side)
When images are formed on the back side
of the mirror they are virtual images.
When you look at a mirror and see an
object back inside it that looks different
than usual you see a virtual image
(looking at a spoon, or car side mirror “objects may appear closer than seem”)
Mirror Equations
Mirror Equations - You can find out where and what an image should look like
by using the mirror equations
To find the distance of the
image from the mirror
1
1 1


f d0 di
To find the Magnification and
Orientation of the Image
M
d i
do
M
hi
ho
Important - when using a convex mirror the focal point (f) must be made negative (-)
Determining the Image
di = (+)
di = (-)
M = (+)
M = (-)
|M|=1
|M|<1
|M|>1
real image
vitual image
upright
inverted (upside down)
same size
smaller
larger
note | M | = (absolute value of M)
Concave mirrors can form any
types of these images
- real or virtual
- smaller, same size, or larger
- inverted or upside down
Convex mirrors can only form
one type of image ALWAYS
- smaller, upright, virtual
Example: A convex mirror with (f = 4 cm, d0 = 8 cm)
1
1 1


f d0 di
Note that the f is (-) since it’s
a convex mirror
1
1 1
 
 4 8 di
 0.25  0.125 
 0.375 
M
M
1
di
1
di
di   2.67 cm
d i
do
 (2.67 cm)
8
M  0.33
di = (-)
so its virtual
M = (+)
so its (upright)
|M|<1
so its smaller
Ray Diagrams (for concave mirrors)
We use ray diagrams to draw a picture of what the image would look like
3 Light rays are drawn all originating from the tip of the OBJECT. The point
where these rays intersect gives the location where the tip of the IMAGE will be
Lets try an example with f = 5 cm, do = 12 cm
The first light ray we draw goes
through the center of curvature of
the mirror
C
This light reflects back upon
itself as if unaffected
f
Ray Diagrams (for concave mirrors)
The second light ray we draw goes
horizontally straight towards the
mirror
C
This light ray reflects back
and passes through the focal
point
f
Ray Diagrams (for concave mirrors)
The third light ray we draw goes
through the focal point before it
hits the mirror
C
This light ray emerges
horizontal when it reflects
from the mirror
f
A concave mirror (converging)
with (f = 2 cm, d0=5 cm)
Putting it all together.
Draw all three rays, and the point where
they intersect represents the point where
the tip of the image will be formed
Describe the image:
Real
Smaller
Inverted
Image
C
Check the math
f
1
1 1


f d0 di
1 1 1
 
2 5 di
M
1
0 . 5  0 .2 
di
0 .3 
1
di
d i  3.33 cm
M
d i
do
 3.33
5
  0.67
di = (+)
so its real
M = (-)
so its inverted
|M|<1
so its smaller
Special Examples
1- When the object is located exactly on (f) the rays will not intersect anywhere and
there will be no image
2- When the object is placed right on C, you can only draw two rays. The first ray
that is supposed to be drawn through point C, cant be drawn because you are located
right on top of it.
C
Image
f
Special Examples
3 - When the object is placed in front of C or in front of F. Special rules apply.
The problem with this case is that the object is in front of the points “f” and “c” so it
is impossible to draw the rays through those points.
So instead, the rays that are supposed to go through those points, are drawn as if the
started there. The first ray is drawn as if it started at C. The second ray is drawn
straight and reflects through f. The third ray is drawn as if it started at f.
We extend the reflected
rays back behind the
mirror to see where they
appear to come from.
This is the image point.
Notice that these rays do
not intersect anywhere
over here
C
Image
f
Describe the image:
Virtual
Larger
Upright
Ray Diagrams (for convex mirrors)
The nice thing about Convex mirrors is that the ray diagrams are ALWAYS,
ALWAYS the same. They are slightly different then the concave mirrors
however and you should be careful to notice the differences. In this type of
mirror, you always have to extend the reflected rays back behind to find the
image
Lets try an example with f = 5 cm, do = 12 cm
The first light ray we draw
goes towards the center of
curvature on the other side
f
C
This light ray reflects back
on itself as if unaffected.
Ray Diagrams (for convex mirrors)
The second light ray we
draw goes horizontally
towards the mirror.
f
C
This light ray reflects back
AS IF it came from point “f”
Ray Diagrams (for convex mirrors)
The third ray goes towards
the f on the back side of the
mirror
f
C
This light ray reflects back
horizontally
Ray Diagrams (for convex mirrors)
Put them all together and extend the reflected rays behind the mirror to find
the object
Notice that these
rays do not intersect
anywhere over here
We extend the reflected
rays back behind the
mirror to see where they
appear to come from.
This is the image point.
Image
f
C
Describe the image:
Virtual
Smaller
Upright
Mirror Defects
The geometry of a spherical mirror is such that distorted blurred images can be
produced by the mirror
Normally, rays that approach the
mirror horizontally reflect
through the focal point
C
If light rays are far from the
principle axis up towards the top
of the mirror, they don’t reflect
as much and actually can reflect
slightly off from the principle axis
f
This produces a blurred image.
This phenomenon is known as
SPHERICAL ABBERATION
Mirror Defects
Correcting Spherical Abberation - The use of a Parabolic mirror eliminates the
problem of Spherical Abberation. A Parabolic mirror has a parabolic rather than
spherical shape.
The parabolic shape assures that
all horizontal rays approaching it
will pass through the focal point
when reflected
C
f
Fini
That’s the end of the mirrors
presentation. If you enjoyed this
film, look for other great
presentations such as
”101 Easy Ways to Fail Physics”
©2001, well not really