UNIT 8
Light and Optics
1
ConcepTest 35.2b
You stand in front of a
mirror. How tall does the
mirror have to be so that
you can see yourself
entirely?
Mirror II
1) same as your height
2) less than your full height but
more than half your height
3) half your height
4) less than half your height
5) any size will do
ConcepTest 35.2b
You stand in front of a
mirror. How tall does the
mirror have to be so that
you can see yourself
entirely?
Mirror II
1) same as your height
2) less than your full height but
more than half your height
3) half your height
4) less than half your height
5) any size will do
Trace the light rays from the
image’s foot to the mirror and then
to the eye. Since we know that qi
= qr , you need a mirror only half
your size.
ConcepTest 35.2c
Mirror III
1) No.
Does this depend on your
distance from the mirror?
2) Yes.
3) Depends on the mirror.
4) Depends on the person.
ConcepTest 35.2c
Mirror III
1) No.
Does this depend on your
distance from the mirror?
2) Yes.
3) Depends on the mirror.
4) Depends on the person.
The further you step back, the
smaller the incident and
reflected angles will be. But the
rays will still be reflected at the
same points, so the ray from the
foot will still be reflected at midheight.
Thursday February 16th
Light and Optics
6
TODAY’S AGENDA
Thursday, February 16
 Curved Mirrors Concave
 Hw: Practice B (all) p462
UPCOMING…
 Fri:
 Mon:
 Tue:
NO School
Curved Mirrors Convex
Problem Quiz #1
Color and Polarization
 Wed: Refraction
7
Chapter 13
Light and Reflection
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).
Formation of Images by Spherical Mirrors
Rays coming from a faraway object are effectively parallel.
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.
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.
Formation of Images by Spherical Mirrors
Using geometry, we find that the focal length is half the radius of
curvature:
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.
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 principal axis; after reflection it passes
through the focal point.
2. A ray through the focal point; after reflection it is parallel to
the principal axis.
3. A ray through the focal point; after reflection it is parallel to
the principal axis.
Images Formed by Spherical Mirrors
Concave Mirror
R
C = center of
curvature
R = radius
C
Principle Focal Point
R
f
2
Images Formed by Spherical Mirrors
Image Characteristics
Type:
Size:
Orientation:
Real or Virtual
Larger, Smaller, or Same (as the Object)
Upright or Inverted
do :
always positive
di:
real is positive; virtual is negative
f:
In front of mirror is positive; Behind mirror is negative
Images Formed by Spherical Mirrors
Concave Mirror
Image Characteristics
Case #1
parallel ray
central ray
real
smaller
focal ray
inverted
image
image found between C and f
Images Formed by Spherical Mirrors
Concave Mirror
Case #2
Image Characteristics
real
same
inverted
image
image found at the C
Images Formed by Spherical Mirrors
Concave Mirror
Case #3
Image Characteristics
real
larger
C
inverted
image
image found beyond C
Images Formed by Spherical Mirrors
Concave Mirror
Case #4
Vampire case
Image Characteristics
No image
C
Images Formed by Spherical Mirrors
Concave Mirror
Case #5
Make-up case
image
C
Image Characteristics
virtual
larger
image found behind mirror
upright
Images Formed by Spherical Mirrors
Concave Mirror
Light Source at
the Focal Point
Produces Parallel Rays of Light
Images Formed by Spherical Mirrors
Concave Mirror
di
do
f
ho
hi
hi di − f
=
ho
f
Images Formed by Spherical Mirrors
Concave Mirror
di
do
f
ho
hi
Images Formed by Spherical Mirrors
hi
ho
hi di  f

ho
f
di  f di

f
do
do di − fdo = fdi →
=
di
do
→ do di − f = fdi
do di = fdi + fdo
Images Formed by Spherical Mirrors
do di = f di +do →
di
do
1
+
=
do di do di f
Images Formed by Spherical Mirrors
Concave Mirror
f
Virtual
Image
Images Formed by Spherical Mirrors
Concave Mirror
do
di
ho
f
hi
hi di + f
=
ho
f
Images Formed by Spherical Mirrors
do
Concave Mirror
ho
di
hi
Magnification
f
M > 1 Larger
M < 1 Smaller
hi
di
M=

ho
do
M = 1 Same
M + Upright
M - Inverted
Images Formed by Spherical Mirrors
A object is placed between a concave mirror and its focal
point. The image formed is
(A) virtual and inverted.
(B) virtual and upright.
(C) real and upright.
(D) real and inverted.
Images Formed by Spherical Mirrors (Problem)
A mirror at an amusement park shows an upright image of any
person who stands 1.4 m in front of it. If the image is three
times the person’s height, what is the radius of curvature?
hi
di
M=

ho
do
di
di
3= 
= 
do
1.4m
The image characteristics identify
the case as concave #5 (larger, virtual,
and upright).
di = -4.2 m
(1.4)(-4.2)
dodi
f
f
1.4 - 4.2
do  di
1 1
1
 
f do (-di)
f  1.45m
R  2.90m
Images Formed by Spherical Mirrors
If you stand in front of a concave mirror, exactly at its focal
point,
(A) you will see your image at your same height.
(B) you won't see your image because there is none.
(B) you will see your image, and you will appear smaller.
(C) you will see your image and you will appear larger.
END
33