Images in Concave
Mirrors
Properties
 The mirror has a
reflecting surface
that curves inward.
 When you look at
objects in the
mirror, the image
appears distorted.
Ray Diagram
 You can apply the
same rules of
reflection for a
plane mirror by
thinking of the
curved surface as
many small, flat
mirrors.
Small, flat
mirrors
Centre of
curvature
 If you draw the
normal for each of
the small mirrors,
they will all meet at
one point called the
centre of curvature
(C) of the mirror.
 The thick, horizontal
normal that touches
the centre of the
mirror is called the
principal axis. It helps
you locate the positions
of objects that are in
front of the mirror.
The point at which the
principal axis cuts the
mirror is called the
vertex (V).
vertex
C
Principal axis
 If an incident ray
passes through the
centre of curvature,
the angle of
reflection will be
zero since it passes
over the normal and
reflects back on
itself.
C
 When the incident
ray is put parallel to
the principal axis, it
intersects the
principal axis at a
point called the
focal point (F).
 The focal length is
the distance
between the vertex
of a mirror and the
focal point.
Rays parallel to
principal axis
Focal length
Focal point
 When drawing a ray diagram to predict
the position of an image, it is helpful
to draw the object so that the bottom
is on the principal axis.
 This means that the bottom of the
image will be on the principal axis too.
 Use the laws of reflection to draw 2
incident rays.
 Trace back the reflected rays to locate
the image point for the top of the
object.
Steps…
 The first ray put through the top of the
object, parallel to the principal axis (it
will pass through the focal point)
 Second ray: through top of object and
through focal point, it should be
parallel to principal axis.
 Third ray: drawn through the centre
point to the top of the object (should
reflect back on itself)
You try it!!
 Follow 10.2 and draw a ray diagram for an
object that is between the focal point and
the mirror. List the characteristics of the
image.
 Follow 10.3 and draw a ray diagram for an
object that is between the centre of
curvature and the focal point. List the
characteristics of the image
 Follow 10.4 and draw a ray diagram for an
object that is behind the centre of curvature
and the focal point. List the characteristics
of the image
Mirror and Magnification
Equations
 You can predict the characteristics of an
image using 2 equations: the mirror equation
and the magnification equation.
 Mirror equation: allows you to calculate the
location of the image.
1 =1 + 1
f
di do
 Magnification: tells you the size/height of
the image relative to the object.
m = hi = -di
ho do
Example:
 Problem: A concave mirror has a focal length
of 12cm. An object with a height of 2.5cm is
placed 40.0cm in front of the mirror.
Calculate the distance and height.
 A) mirror equation: 1 = 1 + 1
f d i do
(rearrange the formula) 1 = 1 - 1
di f
do
(substitute)
1 =1 1
di 12cm 40.0cm
(solve)
di = 17.14cm
 The image is 17cm from the mirror. It
is a positive number, so it will be in
front of the mirror.
 B) Magnification: m = hi = -di
h o do
__hi__ =
-17.14
2.5cm
40.0
hi = -1.07cm
The height is 1.1cm. The image height is
negative, so the image is inverted.
You Try It!!!
 P. 427 # 1-5
 P. 430 # 3-8
Curved Mirrors - CONCAVE
1. Draw object at desired
length away from the
mirror
2. Draw a ray parallel to your
axis until it hits your mirror.
3. Reflect this ray through your
focal point
4. Draw a new light ray that
goes through the focal point
FIRST before it hits the
mirror
5. Reflect this ray parallel to
your axis.
6. At the point of intersection
of your reflected rays is the
top of your new object
CONCAVE Finished Product
Curved Mirrors - CONVEX
1. Draw object in front of your
convex mirror
2. Draw a ray parallel to your
axis until it hits your mirror.
3. The reflected ray needs to be
extended into the virtual
side of your mirror, through
the focal point.
4. Draw a new light ray that
would go through the focal
point if it could. Stop the ray
when it hits in the mirror.
5. Reflect this ray parallel to
your axis
6. At the point of intersection
of your reflected rays is the
top of your new object
CONVEX – Finished Product
SEATWORK FOR TODAY
 Complete a Plain Mirror Ray Diagram for any slanted
object
 Complete a Concave Ray Diagram for an object of
your choice.
 Complete a Convex ray diagram for an object of your
choice.