Calculate distances and focal lengths using the mirror
equation for concave and convex spherical mirrors.
Draw ray diagrams to find the image distance and
magnification for concave and convex spherical mirrors.
Distinguish between real and virtual images.
Differentiate between parabolic mirrors and
spherical mirrors.
Concave Mirrors

A concave spherical mirror is a mirror
whose reflecting surface is a segment of
the inside of a sphere.
 Reflects light from its inner “caved in”

surface
Concave mirrors can be used to form real
images.
Real vs. Virtual Images

A real image is an image formed when
rays of light actually converge and pass
through a point on the image.
 Real images can be projected onto a
screen.

Virtual images are behind a plane
mirror
 The rays reflected never actually converge
but appear to diverge from behind the mirror
The radius of curvature, R, is one factor
that determines the size and where the
image will appear
 R is the distance from the mirror’s surface
to the center of curvature, C
 C is the geometric center of the sphere
 Principle axis is the straight line
perpendicular to the center of the surface
of the mirror

F is the focal point: where the reflected
rays cross the principal axis; parallel rays
converge at F
 f is the focal length of the mirror which is
the distance from F to the mirror along the
principal axis
 2f=R

Locating images in mirrors by ray tracing
1.
Determine scale of drawing
a. If object is beyond F, then image will be on
object side of mirror. Draw mirror on right
side of paper
b. If the object is beyond C, the image
distance will be small, so draw object near
left side of paper
c. If object is between C and F, the image will
be beyond C. The closer the object is to F,
the farther away the image will be, so
image will be near left side of paper
2.
Draw the principal axis.
a. Draw vertical line where principal axis
touches mirror.
b. If the focal point is known, indicate
that position on the principal axis and
label it F.
c. Identify and label center of curvature,
C (it is twice the focal distance, f, from
mirror)
3.
Draw object
4.
5.
6.
7.
Draw ray 1 from top of object parallel to principal
axis. (All rays parallel to principal axis are
reflected through F)
Draw ray 2 from top of object through F. (It will be
reflected parallel to principal axis)
Draw ray 3 from top of object through C.
The image is located where any two rays
intersect. The third ray is used to check. Draw
line to principal axis to represent image
Practice Problem
The focal length is 20.0 cm. Draw a ray
diagram to identify where each image is
formed.
1. Object is at C
2. Object is at F
3. Object is between C and F
4. Object outside C
5. Object inside F

You can use the mirror equation below to
predict the image location.

p and q have a positive value if they are on
the front side or reflecting side of the mirror.
 Real images

q has a negative value if the image is on the
back side of the mirror.
 Virtual image

f is positive for concave mirrors.
h
is positive if it is upright and negative
when inverted.
 M is positive for virtual (upright) images and
negative for inverted images.


Geometry shows that the ratio between image and object
height is the same as the ratio between image and object
distance.
The negative sign is required because images on the
back side of the mirror have negative image distances.
Practice problem
A concave spherical mirror has a focal
length of 10.0 cm. Locate the image of a
pencil that is placed upright 30.0 cm from
the mirror. Find the magnification of the
image. Draw a ray diagram reference.
Spherical aberration
With spherical mirrors, rays not near
the principal axis do not all meet at
the image point (spherical aberration,
which causes blurry images)
 Parabolic mirrors eliminate this
problem and produce sharper images
(reflecting telescopes).
 Paraxial rays are very near the
principal axis, make the assumption
that all the rays in drawings and
calculations are paraxial even if they
may not appear to be.

Convex Mirrors

Spherical mirror whose reflecting
surface is outward-curved segment of a
sphere
 Also called diverging mirror
○ Reflected rays spread out
 Side-view mirrors on cars

Image is always virtual and smaller than
object
 Appears to be farther away
○ “Objects may be closer than they actually
appear”
Convex Ray Diagrams

F is behind the mirror
 Still half way between C and mirror

If using mirror equations, f is negative,
image distance is also negative
Convex Ray Diagrams

Ray 1: from top of object parallel to
principal axis
 Reflected ray: draw dashed line from F to
point where ray 1 strikes mirror, continue line
past mirror

Ray 2: approaches mirror on a path that,
if extended behind mirror, would pass
through F
 Reflected ray: parallel to principal axis,
continue it behind mirror.