Optics
Spherical Mirrors
 Spherical mirror – a section of a sphere of
radius R and with a center of curvature C
R
C
Mirror
Spherical Mirrors
 The radius (R) and center of curvature (C) of the sphere
 Principal axis – a line drawn through C to the mirror
 Vertex (V) – where the principal axis intersects the mirror
 The focal point (F) and focal length (f)
Principal axis
R
f
V
F
C
Spherical Mirrors
 The focal point (f) is halfway between C and V
f=R/2
 R = 2f
Concave (converging) Mirror
Inside surface of the mirror forms a “cave”
Images will form along the focal plane
from incoming rays not parallel to the
principal plane.
Convex/Diverging Mirror
Incoming rays that are parallel to the principal axis are
reflected such that they appear to diverge from the focal point.
This gives the viewer an expanded field of view.
Ray Diagrams
 The first ray is drawn parallel to the principal axis
and is reflected through the focal point (F).
 The second ray is drawn through the center of
curvature (C), to the mirror surface, and is
reflected directly back.
 The intersection of these two rays is the position
of the image.
Ray Diagrams – Concave Mirror
Center of Curvature < Object Distance
C < Do
Real image is inverted (upside down) and smaller
Ray 1 “ focuses” in on the focal point, F, after hitting the mirror.
Ray Diagrams – Concave Mirror
Focal Point < Object Distance
< Center of Curvature
F < Do < C
Real image is inverted (upside down) and larger
Ray Diagrams – Concave Mirror
Object Distance < Focal Point
Do < F
Virtual image is not inverted (right side up) and larger
Image Characteristics
 The characteristics of the images can be
described in the following manner:
 An image may be real or virtual
 An image may be upright or inverted
 An image may be larger or smaller than the
object
Section 7.3
Image Characteristics
 Real image – an image for which the light
rays converge so that an image can be
formed on a screen

Real images form in front of the mirror where a
screen can be positioned
 Virtual image – an image for which the light
rays diverge and cannot form on a screen


Virtual images form behind or inside the mirror
where the light rays appear to converge
A virtual image results when the object is
inside the focal point
Ray Diagrams – Convex Mirror
Always has virtual image that is not inverted (right side up) and smaller
Example – Concave Mirror
 An object is placed 25 cm in front of a
concave mirror with a radius of curvature of
20 cm. Construct the ray diagram.
 Given: C = 20 cm, therefore f = 10 cm
Image Distance:
approximately 17 cm
17 cm
Image Characteristics:
Real image, Inverted, Reduced
Example – Concave Mirror
 An object is placed 15 cm in front of the
concave mirror with a radius of curvature of
20 cm. Construct the ray diagram.
 Given: C = 20 cm, therefore f = 10 cm
Image Distance:
approximately 30 cm
30 cm
Image Characteristics:
Real image, Inverted, Magnified
Lenses
A converging lens is thicker in the middle than at
its rim and brings parallel light to a single point at a
distance called the focal length of the lens.
A diverging lens is thinner in the middle than at its
rim and spreads out parallel light so that it seems to
come from a point behind the lens.
Converging Spherical Lens
 Rays parallel to the principal axis converge at
the focal point on the opposite side of the lens
Ray Diagrams
 The first ray is drawn parallel to the principal
axis and then refracted by the lens through
the focal point of the lens.
 The second ray is drawn through the center
of the lens with no change in direction.
 The tip of the arrow occurs where these two
rays intersect.
Converging Lens - Do > F
 If the object is beyond F, an inverted, real image is
formed.
 The image becomes larger as F is approached.
Object Outside the Focal Point
Do > F
Converging Lens - Do < F
 Inside F, an object always forms a virtual
image on the object side of the lens.
Object Inside the Focal Point
Do < F
Diverging Lens
 The Image is Always Upright and Smaller
than Object
Example - Converging Lenses
 A convex lens has a focal length of 12 cm.
Draw ray diagrams for an object at 18 cm
from the lens.
36 cm
Image Distance:
approximately 36 cm
Image Characteristics:
Real image, Inverted, Magnified
Example - Diverging Lenses
 A convex lens has a focal length of 12 cm.
Draw ray diagrams for an object at 8 cm from
the lens.
Image Distance:
approximately 24 cm
24 cm
Image Characteristics:
Virtual image, Upright, Magnified
How a Camera Works
A camera uses a converging lens to focus light rays from an
object onto the film.
The Eye
 The human eye operates much like a camera
 The lens focuses the object on the retina.
 The image is reduced and inverted. The brain
translates the information.
 Rods for night vision. Cones for color.
The Eye
Normal
Farsighted
Nearsighted
Farsightedness occurs
when the eyeball is too
short or lens of eye is too
thin, focusing the object
behind the retina and
making it difficult to focus
on nearby objects.
Nearsightedness occurs
when the eyeball is too
long or lens of eye is too
thick, focusing the object in
front of the retina and
making it difficult to focus
on distant objects. Lasers
can shave some of the
lens off to correct it.
converging lens
(thicker in middle)
diverging lens
(thicker at edges)
The Eye
Muscles in the eye change the thickness of the lens so
we can focus on objects at different distances.
As a person grows older the lens of the eye becomes
less deformable and therefore cannot focus as readily.
Reading glasses may be required.
Polarization
 Light is usually randomly polarized.
 Polaroid sunglasses can reduce certain
orientations.
Polarization
 Light reflection from the surface of the ground
or water is partially polarized in the horizontal
direction.

These polarized reflections increase the
intensity and are seen as an
annoying/dangerous “glare.”
 Polarizing sunglasses are oriented vertically
and therefore do not allow the horizontal
component of light to pass and thereby
significantly reduce glare.
Summary
 Reflection
 Refraction
 Spherical Mirrors

θr = θi
n = c / cm
f=R/2
Convex (diverging) or Concave (converging)
expanded field
 Lenses

Convex (converging) or Concave (diverging)
thick at center
thick at edge
 Which of the following is true for a concave lens?




(a)
(b)
(c)
(d)
a lens that forms virtual images for Do > f.
a converging lens
a lens that forms real images for Do < f.
thicker at the center than at the edge.
 Which is true for a real image?




(a) It is formed behind a mirror.
(b) It occurs only for D1 = Do
(c) It is always magnified.
(d) It is formed by converging light rays.
 Which is true for a virtual image?




(a) It can be formed on a screen.
(b) It is always formed by a convex lens.
(c) It is formed on the object side of a lens.
(d) It cannot be formed by a concave lens.
 Which is true for a convex mirror?




(a)
(b)
(c)
(d)
It is a converging mirror.
It has a radius of curvature equal to f.
It forms magnified and reduced images.
It forms only virtual images.