Do Now
1. A ray of light is incident towards a plane
mirror at an angle of 30-degrees with the mirror
surface. What will be the angle of reflection?
2. If Suzie stands 3 feet in front of a plane mirror,
how far from the person will her image be
located?
23.3 Formation of Images by Spherical
Mirrors
Spherical mirrors are shaped like sections of
a sphere, and may be reflective on either the
inside (concave) or outside (convex).
23.3 Formation of Images by Spherical
Mirrors
Rays coming from a faraway object are
effectively parallel.
23.3 Formation of Images by Spherical
Mirrors
Parallel rays striking
a spherical mirror do
not all converge at
exactly the same
place if the curvature
of the mirror is large;
this is called
spherical aberration.
23.3 Formation of Images by Spherical
Mirrors
If the curvature is small, the focus is much more
precise; the focal point is where the rays
converge.
Terms
• The point in the center of
the sphere from which
the mirror was sliced is
known as the center of
curvature and is
denoted by the letter C
• The point on the mirror's
surface where the
principal axis meets the
mirror is known as the
vertex and is denoted by
the letter A
Terms
• The vertex is the geometric
center of the mirror. Midway
between the vertex and the
center of curvature is a point
known as the focal point; the
focal point is denoted by the
letter F.
• The distance from the vertex
to the center of curvature is
known as the radius of
curvature (represented by R).
The radius of curvature is the
radius of the sphere from
which the mirror was cut.
Terms
• the distance from the
mirror to the focal point is
known as the focal
length (represented by f).
• Since the focal point is
the midpoint of the line
segment adjoining the
vertex and the center of
curvature, the focal length
would be one-half the
radius of curvature.
23.3 Formation of Images by Spherical
Mirrors
Using geometry, we find that the focal length is
half the radius of curvature:
(23-1)
Spherical aberration can be avoided by
using a parabolic reflector; these are more
difficult and expensive to make, and so are
used only when necessary, such as in
research telescopes.
1.Check Your Understanding:
• The surface of a concave mirror is pointed
towards the sun. Light from the sun hits the
mirror and converges to a point. How far is this
converging point from the mirror's surface if the
radius of curvature (R) of the mirror is 150 cm?
• Answer: 75 cm
• If the radius of curvature is 150 cm. then the
focal length is 75 cm. The light will converge
at the focal point, which is a distance of 75
cm from the mirror surface.
2. Check Your Understanding:
• It's the early stages of a concave mirror lab.
Your teacher hands your lab group a concave
mirror and asks you to find the focal point. What
procedure would you use to do this?
• You will need to measure the distance from the
vertex to the focal point. But first you must find
the focal point. The trick involves focusing light
from a distant source (the sun is ideal) upon a
sheet of paper. Once you find the focal point,
make your focal length measurement.
Formation of Image
• Upon reflecting, the
light will converge at a
point. At the point
where the light from
the object converges,
a replica, likeness or
reproduction of the
actual object is
created. This replica
is known as the
image.
23.3 Formation of Images by Spherical
Mirrors
We use ray diagrams to determine where an
image will be. For mirrors, we use three key
rays, all of which begin on the object:
1. A ray parallel to the axis; after reflection it
passes through the focal point
2. A ray through the focal point; after reflection
it is parallel to the axis
3. A ray perpendicular to the mirror; it reflects
back on itself
23.3 Formation of Images by Spherical
Mirrors
23.3 Formation of Images by Spherical
Mirrors
The intersection of these three rays gives the
position of the image of that point on the
object. To get a full image, we can do the
same with other points (two points suffice for
many purposes).
Object Located Beyond Center
of Curvature
Object Located at the center of
Curvature
Object is Located Between Center of Curvature and
Focal Point
Object is Located in Front of
Focal Point
Do Now
If a concave mirror produces a real image, is
the image necessary inverted? Explain.
23.3 Formation of Images by Spherical
Mirrors
If an object is outside the center of curvature of a
concave mirror, its image will be inverted,
smaller, and real.
23.3 Formation of Images by Spherical
Mirrors
If an object is inside the focal point, its image
will be upright, larger, and virtual.
Image Characteristics for
Concave Mirrors
L – location
O – orientation
S – relative size
T - type
1) Between C and F, inverted,
reduced, real
2) At C, inverted, same
size, real
3) Beyond C, inverted,
magnified, real
4) No image
5) Beyond mirror,
upright, magnified,
virtual
Convex Mirror
A convex mirror is sometimes referred to as
a diverging mirror due to the fact that
incident light originating from the same point
and will reflect off the mirror surface and
diverge.
23.3 Formation of Images by Spherical
Mirrors
For a convex mirror,
the image is always
virtual, upright, and
smaller.
Image Characteristics for
Convex Mirrors
• Convex mirrors always produce virtual upright reduced in
size images. The location of the object does not affect
the characteristics of the image.
23.3 Formation of Images by Spherical
Mirrors
Geometrically, we can derive an
equation that relates the object
distance, image distance, and
focal length of the mirror:
(23-2)
23.3 Formation of Images by Spherical
Mirrors
We can also find the magnification (ratio of
image height to object height).
(23-3)
The negative sign indicates that the image is
inverted. This object is between the center of
curvature and the focal point, and its image is
larger, inverted, and real.
The +/- Sign Conventions
The sign conventions for the given quantities in the mirror
equation and magnification equations are as follows:
• f is + if the mirror is a concave mirror
• f is - if the mirror is a convex mirror
• di is + if the image is a real image and located on the
object's side of the mirror.
• di is - if the image is a virtual image and located behind
the mirror.
• hi is + if the image is an upright image (and therefore,
also virtual)
• hi is - if the image an inverted image (and therefore, also
real)
23.3 Formation of Images by Spherical
Mirrors
Problem Solving: Spherical Mirrors
1. Draw a ray diagram; the image is where the rays
intersect.
2. Apply the mirror and magnification equations.
3. Sign conventions: if the object, image, or focal point is
on the reflective side of the mirror, its distance is
positive, and negative otherwise. Magnification is
positive if image is upright, negative otherwise.
4. Check that your solution agrees with the ray diagram.