Concave Mirrors
Reflection, Image Height, and
Distance
What is a concave mirror
• Imagine a large hollow sphere, with a
mirror finish on the inside.
• Cut a square out of the sphere’s shell and
look at the mirrored side.
Mirror
Ray Diagram
• A Ray Diagram will tell you what a
reflection will look like in the mirror without
having to actually look into it…
Parts of Ray Diagrams
• Start out with a concave mirror and a line
going straight to the middle.
• This will be called the Principal Axis
Mirror
Principal Axis
Center of Curvature
• Imagine if the mirror was a whole circle…
The center of that circle, would
be the Center of Curvature ‘C’
C
Focal Point
• Def: A specific point where all light rays
parallel to the principal axis are reflected
to by the concave mirror.
F is always closer
to the mirror than
C.
Focal Point (F)
Principal Axis
C
Center of Curvature
Laws of Reflection
• There are two rules to tell us how light will
reflect when it hits a curved mirror
Laws of Reflection for Concave
Mirrors
• Law 1: Any incident light ray parallel to
the principal axis, will reflect through the
focal point.
Principal Axis
F
Laws of Reflection for Concave
Mirrors
• Law 2: Any incident ray of light passing
through the focal point will reflect parallel
to the principal axis.
Principal Axis
F
Drawing a Ray Diagram- Step 1
Situation 1: An object is outside of the focal point
and the center of curvature.
C
F
Draw the mirror, the principal axis,
the focal point and the object.
Drawing a Ray Diagram- Step 1
Situation 1: An object is outside of the focal point
and the center of curvature.
C
F
Before we begin drawing the
diagram we must consider the two
Laws of Reflection for Concave
Mirrors
Drawing Ray Diagrams- Step 2
• Apply one Law: From the TOP of the
object- Incoming ray is parallel to the
principal axis and is reflected through the
focal point…
C
F
Drawing Ray Diagrams- Step 3
• Apply the other Law: From the TOP of the
object- Incoming ray goes through the
focal point and is reflected back parallel to
the principal axis…
C
F
Drawing Ray Diagrams- Step 4
• Where the red lines (reflected beams of
light) cross will be where the top of the
pencil appears to be in the reflection you
see in the mirror…
C
F
Drawing Ray Diagrams- Step 4
• So draw in the pencil. Note: The bottom
of the pencil will ALWAYS be resting on
the principal axis!
Real Pencil
C
Pencil’s Reflection
F
Situation 1
• When the object is outside C and F, the
reflected image is smaller and inverted
than the actual object.
This reflected
image is called a
real image,
because it is
formed in front of
the mirror.
C
F
Situation 2
• Now, consider the situation where the
object is located at C.
Sketch a ray diagram to
determine where the
image would be located
and how it’s size would
change.
F
C
Situation 2
The image is still inverted,
but is the same size as the
actual object, and located
directly underneath it.
C
F
Situation 3
• What if the object is located between C
and F?
Sketch a ray diagram to
determine where the
image would be located
and how it’s size would
change.
F
C
Situation 3
Image is inverted,
magnified larger than the
actual object, and
appears farther away
than the original.
F
C
Situation 4
• The object is located on the focal point.
The reflected rays never
overlap, so no image is
formed. An object sitting at
the focal point of the mirror
“disappears” in the mirror.
C
F
The Mirror Equation
• Consider a basic ray diagram:
Real Pencil
F
Pencil’s Reflection
The Mirror Equation
• Consider a basic ray diagram:
• The focal point is “f”
Real Pencil
F
Pencil’s Reflection
The Mirror Equation
• Consider a basic ray diagram:
• The object distance is “p”:
Real Pencil
p
f
Pencil’s Reflection
The Mirror Equation
• Consider a basic ray diagram:
• The image distance is “q”:
Real Pencil
p
f
Pencil’s Reflection
q
The Mirror Equation
• Consider a basic ray diagram:
• Focal length: f
• Object distance: p
• Image distance: q
Real Pencil
p
f
Pencil’s Reflection
q
The Mirror Equation
• Putting these three together gives the
relationship we call the Mirror Equation:
• Focal length: f
1 1 1
• Object distance: p
 
• Image distance: q
p q f
Magnification
• Mirrors also change the size of objects.
• How much it changes the size is called the
Magnification of the mirror.
Magnification
• Magnification is a ratio of the object and
the image’s:
a) height
or
b) distance
Either one will give you the magnification.
Magnification
• Let’s look at the ray diagram again:
• ‘p’ and ‘q’ are still the same.
Real Pencil
p
f
Pencil’s Reflection
q
Magnification
• Let’s look at the ray diagram again:
• ‘h’ is the object’s height:
Real Pencil
h
p
f
Pencil’s Reflection
q
Magnification
• Let’s look at the ray diagram again:
• ‘h' ’ is the object’s height:
Real Pencil
p
h
f
Pencil’s Reflection
h'
q
Magnification
• The equation for magnification relates all
these variables by:
h
q

h
p
Practice
• Using these two equations together can be
used to find out anything you want to know
about an object’s reflection:
•
1)
1 1 1
 
p q f
2)
h
q

h
p
Practice
• Pg. 463 Practice B 1-3 ONLY!