Chapter 18: Mirrors and Lenses
Section 18.1 Mirrors
A plane mirror is a flat, smooth surface from which light is reflected by regular reflection
rather than by diffuse reflection. Light rays are reflected with equal angles of incidence
and reflection.
A plane mirror produces a virtual image which appears to be an equal distance behind the
mirror. With a virtual image, the light rays do not actually converge on the point where
the image appears. The object and the image have the same size. They are pointing in
the same direction, so the image is an erect image. Left and right are reversed which is to
say “the front and back of the image are reversed.”
If you blink your right eye, your mirror image left eye blinks back at you:
Concave Mirrors
A concave mirror reflects light from its inner, (“caved in”) surface. The principle axis
is the straight line perpendicular to the surface of the mirror at its center. The focal point
is the point where all rays parallel to the principal axis meet. It is half the distance
between the mirror and the center of curvature. If you point the principal axis of a
concave mirror at the sun, all the rays (which are parallel to each other—at
“infinity”) will be reflected through the focal point. The distance from the focal
point to the mirror along the principal axis is the focal length, f, of the mirror.
Real vs. Virtual Images:
Real Image:
 the rays actually converge and pass through the image
 it can be seen on a piece of paper
Virtual Image:
 The rays do not converge at the location of the virtual image
 The virtual image cannot be projected on a screen
Drawing Ray Diagrams:
Draw the mirror, principal axis, a vertical line where the principal axis touches the
mirror, the image, the focal point (F) and the center of curvature (C).
 Ray 1 (the parallel ray) is from the object to the mirror parallel to the
principal axis. The reflected ray goes through the focal point
 Ray 2 (the focus ray) is from the object through the focal point. The reflected ray
is parallel to the principal axis
 Where Ray 1 and Ray 2 intersect is the location of the image.
Possible scenarios for concave mirrors:
(see the table that follows)
Object is closer than F Image is virtual, upright and enlarged
Object:
Image:
Location Location
infinity At F
Real/virtual
Real
Orientation
Inverted
>C
at C
Real
Real
Inverted
Inverted
Real
NA
virtual
Inverted
NA
Erect
C-F
at C
C-F
>C
at F
no image
F-mirror Behind
mirror
size
Much
reduced
Reduced
Same as
object
enlarged
none
enlarged
Lens/mirror equation: “If I do I die.”
where f = focal length
d o = distance along the principal axis from the object to mirror
d i = distance along the principal axis from the image to mirror/lens
If solving for f:
magnification is the ratio of the size of the image, h i , to the size of the object, ho
Another useful relationship:
Page 422
b. How high is the image?
Virtual Images Formed by Concave Mirrors
P 424:
P 425, Practice Problems 1-5
Image defects in concave mirrors
Spherical aberration
Convex Mirrors
 A convex mirror is a spherical mirror that reflects light from its outer surface.
 Rays reflected from a convex mirror always diverge.
 Focal length, f, is a negative number
 di is negative because the image is behind the mirror
 Convex mirrors do not form real images.
 Images are reduced in size and so appear far away
 “Fisheye lens” the image is small (reduced) but wide ranging (enlarged) field of
view
 upright image, virtual, reduced (images seem farther away)
 Good for security mirrors & rearview mirrors in cars
Problem from Opening Page: Four Butterflies but only one is real.
Identify the images and the shape of lenses that produced them:
P 427
P 427, Practice Problems 6-8
18.2 Lenses
A lens is made of transparent material, such as glass or plastic, with a refractive index
larger than that of air. Each of the lens’s two faces is part of a sphere and can be convex,
concave, or flat.
Convex lens: (see 6 cases for do in convex lenses worksheet)
 Thicker at the center than at the edges
 Converging lens (they refract parallel light rays so that the light rays meet)
P 431
P 432, Practice Problems 9-11
Object:
Image:
Location Location
infinity At F
Real/virtual
Real
Orientation
Inverted
>2F
Real
Inverted
2F-F
size
Much
reduced
Reduced
at 2F
at 2F
Real
Inverted
2F-F
at F
F-lens
>2F
no image
Behind
mirror
Real
NA
virtual
Inverted
NA
Erect
Why Use A Larger Lens? (see a and b below)
More light will go thru a larger lens:
 Brighter
 Easier to see
P 434:
Page 435, Practice Problems 12-14
Same as
object
enlarged
none
enlarged
Concave lens





Thinner in the middle than at the edges
Diverging lens (rays passing through it spread out)
The image is on the same side of the lens as the object
The image is virtual, erect, reduced in size (no matter how far object is from lens)
Focal length is negative
Defects of Lenses:
Spherical Aberration
Light rays that pass through the extreme edges of lenses do not meet at focal point
Fix: in cameras, use only the center of the lens; in telescopes—use a combination of
convex and concave lenses—Hubble Telescope had to have a fix for spherical aberration
of its main mirror—images were fuzzy from launch in 1990 to fix in 1993
Chromatic Aberration
Light rays that pass through the extreme edges of lenses disperse as the edge of the lens
acts as a prism
Fix: join a convex lens with a concave lens with different index of refraction (this
combination is called an achromatic lens)—used in all precision optical instruments
How the Eye Works:
Vision Defects:
Nearsightedness:
 (a)Light focuses before the retina
 Cannot see distant objects
 Gets worse as the body grows
 (b)Fix: concave lens which will focus the light back on the retina
Farsightedness:
 (c)Light focuses behind the retina
 Cannot see close objects
 Gets worse as the body ages (40+): lens is less flexible
 (d)Fix: convex lens which will focus the light back on the retina