Convex Mirrors – Diverging
Rays are reflected and diverge, giving the illusion that the rays
originated inside the mirror.
Diverging mirrors always produce virtual images that are smaller
then the object.
Ray Diagrams for Convex Mirrors
Incident Ray
Reflected Ray
Parallel to
principal axis
Reflects out as
though coming
from focus
Directed at focus
Reflects back
parallel to
principal axis
Directed at
centre of
curvature
Reflects straight
back on itself
To vertex
Point acts like
plane mirror
i  r
i
r
F
C
F
C
F
C
F
C
Examples – Locate the image for each convex mirror
F
C
F
C
Observations
S smaller
A upright
L
Closer to mirror then object
T virtual
Observations
S smaller
A upright
L
closer
T virtual
http://www.phys.ufl.edu/~phy3054/light/mirror/applets/convmir/Welcome.html
Calculations for Curved Mirrors
1
1 1


The curved mirror equation: f
d o di
where d o is the object distance, d i is the image distance, and f is
the focal length.
d
h
i
i
Magnification Formula: m   d or m  h
o
o
ho d i
h


which leads to i
do
where hi is the height of the image and ho is the height of the
object.
In optics, the negative sign is used to indicate virtual distances
(image and focal point) and inverted heights. Based on the values
and information given, you will likely need to insert the negative sign
yourself.
f is negative
diverging
mirror
converging
d i is negative
Is object
inside f?
NO
When is the image
inverted?
d i is positive
yes
d i is negative
Example 1 – A concave mirror with a 20 cm focal length has a candle
placed in front of it 30 cm from the vertex. Find the image
position and the magnification for this situation.
Given: do  30cm
f  20cm
1
1 1


f d o di
1 1 1
 
di f d o
1
1
1


d i 20 30
di  ?
m
di
do
60
30
m  2
m
1
 0.017
di
d i  60cm
Magnification is negative
so image is inverted
Image distance is
positive so image is real
Example 2 – For the example above, the object is moved to 5.0 cm
from the vertex. Find the image position and magnification.
Example 3 – Given a convex mirror with focal length 20 cm, a candle
is placed 5.0 cm away from the vertex. Find the image position and
magnification.
Applications of curved mirrors
Most technology that involves converging mirrors rely on their
ability to focus the incoming light at a single point.
Newtonian Reflecting Telescope




Light enters the telescope in parallel rays.
These rays are reflected from a concave mirror to a diagonal plane mirror.
The diagonal plane mirror reflects the light to an eyepiece.
The larger the diameter of the mirror, the brighter the light at the focus.
Simple Microscope
Use converging mirror to focus light from within a room through
specimens.
Dentist’s Lamp



The light bulb is placed at the focal point.
Light rays reflect off a parabolic mirror and parallel beams of light project
outward.
The parallel light rays provide uniform illumination resulting in no shadows.
Shadows sometimes are mistaken for cavities.
Shaving Mirror


Shaving or makeup mirrors must be concave and have a long focal length.
Your face must be inside the focal point so that the image of your face is
virtual, upright, and larger.
Solar Furnace




Concave mirror focuses the sun’s rays to a focal point.
Usually water is run through a tube at the focal point and heated by the
converging rays.
The hot water can be used to turn a turbine producing electricity or heat a
building.
Solar ovens use the same principle to heat food.
Satellite Dish



..........
A concave “dish” or reflector is used to reflect TV signals to a central focal
point.
These signals are then relayed to a receiver and your TV set.
Concave reflectors are used for picking up radio waves from space and
telecommunication signals on earth.
Diverging mirrors are used because they contain more visual
information then regular mirrors, hence they give a wider angle of
view.
Security Mirror


Stores use convex mirrors to provide a wide field of view for security.
Convex mirrors always produce virtual, upright, and smaller images.
..........
..
2. Rear view mirrors



Some cars, buses, and trucks use convex mirrors on one of the rear view
mirrors.
Convex mirrors produce a wider field of view, thereby providing the driver more
view in all directions.
Our brain interprets small objects as always being farther away than large
objects. Because the convex mirror produces smaller images, we assume that
the object must be far away. Therefore, some mirrors have a message saying
that objects are closer than they appear.
..........
Funhouse Mirror


Combinations of concave and convex mirrors, often cylindrical, produce funny
images.
The images can portray you as very short and fat, very tall and thin, or
combinations of the two.
..........
Diverging Mirrors
1.
Describe three uses for convex mirrors. (you may need internet resources)
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2.
Complete the following ray diagrams.
F
F
3.
Draw a scale diagram to determine the characteristics of the image formed by a
+5 cm tall object that is place 6 cm in front of a convex mirror with a focal
length of 3 cm.
4.
A diverging mirror has a focal length of 25.0 cm. Locate the image when a +10
cm tall object is placed 26.0 cm in front of the mirror. Describe the image.
5.
Calculate the image positions and magnifications for an object 3 cm tall and a
mirror of focal length +12 cm with the object at 2.5f, 2f, 1.5f, f, 0.5f. (where 2f
means 2x the focal length)
6.
Calculate the image positions and magnifications for an object 3 cm tall and a
mirror of focal length -12 cm with the object at 2f, f, 0.5f.