Chapter 34
A clear sheet of polaroid is placed on top of a similar sheet so that their
polarizing axes make an angle of 30◦ with each other. The ratio of the
intensity of emerging light to incident unpolarized light is:
Images
One of the most important uses of the basic laws governing light is the
production of images. Images are critical to a variety of fields and industries
ranging from entertainment, security, and medicine
A. 1/4
B. 1/3
C. 1/2
D. 3 /4
E. 3 /8
In this chapter we define and classify images, and then classify several basic
ways in which they can be produced.
34- 1
2
Two Types of Images
A Common Mirage
Light travels faster through warm air → warmer air has smaller index of
refraction than colder air → refraction of light near hot surfaces
For observer in car, light appears to be coming from the road top ahead, but is
really coming from sky.
real image
object
lens
object
mirror
virtual image
Image: a reproduction derived from light
Real Image: light rays actually pass through image, really exists in space (or on
a screen for example) whether you are looking or not
Virtual Image: no light rays actually pass through image. Only appear to be
coming from image. Image only exists when rays are traced back to perceived
34- 3
location of source
Fig. 34-1
34- 4
Plane Mirrors, Point Object
Plane Mirrors, Extended Object
Plane mirror is a flat reflecting surface.
Each point source of light in the
extended object is mapped to a
point in the image
Identical triangles
Fig. 34-2
Ib = Ob
Fig. 34-3
Plane Mirror:
Fig. 34-4
Fig. 34-5
i = −p
Since I is a virtual image i < 0
34- 5
34- 6
1
plane
Plane Mirrors, Mirror Maze
Your eye traces incoming rays straight
back, and cannot know that the rays may
have actually been reflected many times
1
2 8
7
9
3 6
Spherical Mirrors, Making a Spherical Mirror
Plane mirror → Concave Mirror
1. Center of Curvature C:
in front at infinity → in front but closer
2. Field of view
wide → smaller
3. Image
i=p → |i|>p
4. Image height
image height = object height → image height > object height
concave
1
2
4
5
Plane mirror → Convex Mirror
1. Center of Curvature C:
in front at infinity → behind mirror and closer
2. Field of view
wide → larger
3. Image
i=p → |i|<p
4. Image height
image height = object height → image height < object height
3
4
5
convex
6
7
8
9
Fig. 34-6
34- 7
Fig. 34-7
Spherical Mirrors, Focal Points of Spherical Mirrors
concave
34- 8
Images from Spherical Mirrors
Start with rays leaving a point on object, where they intersect, or appear to
intersect marks the corresponding point on the image.
convex
Fig. 34-9
Fig. 34-8
Real images form on the side where the object is located (side to which light is
going). Virtual images form on the opposite side.
Spherical Mirror:
f =
1
r
2
r > 0 for concave (real focal point)
r < 0 for convex (virtual focal point)
Spherical Mirror:
1 1 1
+ =
p i f
34- 9
Locating Images by Drawing Rays
h'
h
i
Lateral Magnification: m = −
p
Lateral Magnification:
m =
34-10
Proof of the magnification equation
Similar triangles (are angles same)
Fig. 34-10
Fig. 34-10
1.
2.
3.
4.
A ray parallel to central axis reflects through F
A ray that reflects from mirror after passing through F, emerges parallel to central axis
A ray that reflects from mirror after passing through C, returns along itself
A ray that reflects from mirror after passing through c is reflected symmetrically about the
central axis
34- 11
de cd
=
ab ca
→m=−
cd = i , ca = p ,
i
p
de
= −m
ab
(magnification)
34-12
2
Thin Lenses
Spherical Refracting Surfaces
Converging lens
Fig. 34-11
Diverging lens
Fig. 34-13
Real images form on the side of a refracting surface that is opposite the object (side to
which light is going). Virtual images form on the same side as the object.
Spherical Refracting Surface:
n1 n2 n2 − n1
+ =
p i
r
Thin Lens:
When object faces a convex refracting surface r is positive. When it faces a concave
surface, r is negative. CAUTION: Reverse of of mirror sign convention!
34-13
Images from Thin Lenses
1 1 1
= +
f
p i
Thin Lens in air:
1 1
1
= ( n − 1)  − 
f
 r1 r2 
Lens only can function if the index of the lens is
different than that of its surrounding medium
34-14
Locating Images of Extended Objects by Drawing Rays
Fig. 34-14
Real images form on the side of a lens that is opposite the object (side to which light is
going). Virtual images form on the same side as the object.
34-15
Two Lens System
i1
p2
p1
Lens 1
I1
O2
1. A ray initially parallel to central axis will pass through F2
2. A ray that initially passes through F1, will emerge parallel to central axis
3. A ray that initially is directed toward the center of the lens will emerge from the lens
with no change in its direction (the two sides of the lens at the center are almost
parallel)
34-16
A football field is about 100 meters long. The time for light to travel this
distance is about:
A. 0.33x10-6 s
D. 3 hr
i2
O
Fig. 34-15
B. 0.33 ms
E. 3 yr
C. 33 min
I2
Lens 2
1. Let p1 be the distance of object O from Lens 1. Use equation and/or
principle rays to determine the distance to the image of Lens 1, i1.
2. Ignore Lens 1, and use I1 as the object O2. If O2 is located beyond Lens 2,
then use a negative object distance p1. Determine i2 using the equation
and/or principle rays to locate the final image I2.
The net magnification is: M = m1m2
34-17
18
3
Optical Instruments, Simple Magnifying Lens
Optical Instruments, Compound Microscope
O close to F1
Can make an object appear larger
(greater angular magnification) by
simply bringing it closer to your eye.
However, the eye cannot focus on
objects closer that the near point
pn~25 cm→BIG & BLURRY IMAGE
Mag. Lens
Fig. 34-17
A simple magnifying lens allows the
object to be placed close by making a
large virtual image that is far away.
Simple Magnifier:
mθ ≈
I close to F1’
mθ =
θ=
25 cm
f
Object at F1
Fig. 34-18
m=−
θ'
θ
i
s
=−
p
f ob
M = mmθ = −
h
h
and θ ' ≈
25 cm
f
since i ≈ s and p ≈ f ob
s 25 cm
f ob f ey
34-19
Optical Instruments, Refracting Telescope
34-20
Three Proofs, The Spherical Mirror Formula
β = α + θ and γ = α + 2θ
I close to F2
and F1’
→ θ = β −α =
α≈
Mag. Lens
Fig. 34-19
mθ = −
θ ey
θ ob
→ mθ = −
magnification compounded (microscope)
, θ ob =
f ob
f ey
h'
f ob
, θ ey ≈
ac ac
ac ac
, β=
=
=
cO p
cC r
ac ac
=
CI
i
1
f = r →r =2f
2
γ =
Fig. 34-20
h'
f ey
1
(γ − α ) → α + γ = 2 β
2
ac ac
ac
1 1 1
+
→ + =
=2
p
i
2f
p i f
(telescope)
34-21
34-22
Three Proofs, The Thin Lens Formulas
Three Proofs, The Refracting Surface Formula
n1 sin θ1 = n2 sin θ 2
n1θ1 ≈ n2θ 2 if θ1 and θ 2 are small
θ1 = α + β and β = θ 2 + γ
n1 (α + β ) = n2 ( β − γ )
→ n1α + n2γ = ( n2 − n1 ) β
α≈
Fig. 34-21
Fig. 34-22
n1 n2 n2 − n1
+ =
p i
r
where n1 = 1 and n2 = n
ac
ac
ac
; β=
; γ ≈
p
r
i
1 n n −1
+ =
( Eq. 34-22 )
p' i'
r'
p '' = i '+ L
n
1 1− n
n 1
n −1
+ =
; if L small → + = −
( Eq. 34-25 )
i '+ L i ''
r ''
i ' i ''
r ''
1 1
1 1
1 1
1 1
( Eq. 34-22 ) + ( Eq. 34-25 ) → + = ( n − 1)  −  → + = ( n − 1)  − 
p ' i ''
p i
 r ' r '' 
 r ' r '' 
ac
ac
ac
n1 + n2
= ( n2 − n1 )
p
i
r
n1 n2 n2 − n1
→ + =
p i
r
34-23
34-24
4
The time for a radar signal to travel to the Moon and back, a one-way
distance of about 3.8 × 108 m, is:
Light of uniform intensity shines perpendicularly on a totally absorbing
surface, fully illuminating the surface. If the area of the surface is decreased:
A. 1.3 s
A. the radiation pressure increases and the radiation force increases
B. the radiation pressure increases and the radiation force decreases
C. the radiation pressure stays the same and the radiation force increases
D. the radiation pressure stays the same and the radiation force decreases
E. the radiation pressure decreases and the radiation force decreases
B. 2.5 s
E. 1 × 106 s
C. 8 s
D. 8min
Radio waves of wavelength 3 cm have a frequency of:
A. 1MHz
000MHz
B. 9MHz
C. 100MHz
E. 900MHz
D. 10,
The light intensity 10m from a point source is 1000W/m2. The intensity
100m from the same
source is:
A. 1000W/m2
E. 0.1W/m2
B. 100W/m2
C. 10W/m2
D. 1W/m2
25
26
5