6. 24.2TheElectromagneticSpectrum
Example 1 The Wavelength of Visible Light
Find the range in wavelengths for visible light in the frequency range
between 4.0x1014Hz and 7.9x1014Hz.
nm
750
m
10
5
.
7
Hz
10
4.0
s
m
10
00
.
3 7
14
8
=
=
=
= −
f
c
nm
380
m
10
8
.
3
Hz
10
7.9
s
m
10
00
.
3 7
14
8
=
=
=
= −
f
c
7. 24.3TheSpeedof Light
( )
( )( )
s
m
10
00
.
3
A
m
T
10
4
m
N
C
10
85
.
8
1
1 8
7
2
2
12
=
=
=
−
−
o
o
c
Maxwell’s prediction of the speed of light
9. 25.1 Wave Fronts and Rays
A hemispherical view of
a sound wave emitted by a
pulsating sphere.
The rays are perpendicular
to the wave fronts.
10. 25.1 Wave Fronts and Rays
At large distances from the source, the wave fronts become
less and less curved.
11. 25.2 The Reflection of Light
LAW OF
REFLECTION
The incident ray, the
reflected ray, and the
normal to the surface
all lie in the same
plane, and the angle
of incidence equals
the angle of reflection.
12. 25.2 The Reflection of Light
In specular reflection, the reflected rays are parallel to each
other.
13. 25.3 The Formation of Images by a Plane Mirror
The person’s right hand becomes
the image’s left hand.
The image has three properties:
1. It is upright.
2. It is the same size as you are.
3. The image is as far behind the m
mirror are you are in front of it.
14.
15. 25.3 The Formation of Images by a Plane Mirror
A ray of light from the top of the chess piece reflects from the mirror.
To the eye, the ray seems to come from behind the mirror.
Because none of the rays actually emanate from the image, it is
called a virtual image.
16. 25.3 The Formation of Images by a Plane Mirror
The geometry used to show that the image distance is equal
to the object distance.
17. 25.3 The Formation of Images by a Plane Mirror
Conceptual Example 1 Full-Length Versus Half-Length Mirrors
What is the minimum mirror height necessary for her to see her full
image?
18. 25.3 The Formation of Images by a Plane Mirror
Conceptual Example 2 Multiple Reflections
A person is sitting in front of two mirrors that intersect at a right angle.
The person sees three images of herself. Why are there three, rather
than two, images?
19. 25.4 Spherical Mirrors
If the inside surface of the spherical mirror is polished, it is a concave
mirror. If the outside surface is polished, is it a convex mirror.
The law of reflection applies, just as it does for a plane mirror.
The principal axis of the mirror is a straight line drawn through the
center and the midpoint of the mirror.
20. 25.4 Spherical Mirrors
A point on the tree lies on the principal axis of the concave mirror.
Rays from that point that are near the principal axis cross the axis
at the image point.
21. 25.4 Spherical Mirrors
Light rays near and parallel to the principal axis are reflected
from the concave mirror and converge at the focal point.
The focal length is the distance between the focal point and
the mirror.
22. 25.4 Spherical Mirrors
The focal point of a concave mirror is halfway between
the center of curvature of the mirror C and the mirror at B.
R
f 2
1
=
23. 25.4 Spherical Mirrors
Rays that lie close to the principal axis are called paraxial rays.
Rays that are far from the principal axis do not converge to a single
point. The fact that a spherical mirror does not bring all parallel
rays to a single point is known as spherical abberation.
26. 25.4 Spherical Mirrors
R
f 2
1
−
=
When paraxial light rays that are parallel to the principal axis
strike a convex mirror, the rays appear to originate from the focal
point.
27. 25.5 The Formation of Images by Spherical Mirrors
CONCAVE MIRRORS
This ray is initially parallel to the principal axis
and passes through the focal point.
This ray initially passes through the focal point,
then emerges parallel to the principal axis.
This ray travels along a line that passes through
the center.
28. 25.5 The Formation of Images by Spherical Mirrors
Image formation and the principle of reversibility
29. 25.5 The Formation of Images by Spherical Mirrors
When an object is located between the focal point and a concave mirror,
and enlarged, upright, and virtual image is produced.
30. 25.5 The Formation of Images by Spherical Mirrors
CONVEX MIRRORS
Ray 1 is initially parallel to the principal axis and appears to originate from
the focal point.
Ray 2 heads towards the focal point, emerging parallel to the principal axis.
Ray 3 travels toward the center of curvature and reflects back on itself.
31. 25.5 The Formation of Images by Spherical Mirrors
The virtual image is diminished in size and upright.
32. 25.6 The Mirror Equation and Magnification
length
focal
=
f
distance
object
=
o
d
distance
image
=
i
d
ion
magnificat
=
m
33. 25.6 The Mirror Equation and Magnification
These diagrams are used
to derive the mirror equation.
f
d
d i
o
1
1
1
=
+
o
i
o
i
d
d
h
h
m −
=
=
34.
35. 25.6 The Mirror Equation and Magnification
Example 5 A Virtual Image Formed by a Convex Mirror
A convex mirror is used to reflect light from an object placed 66 cm in
front of the mirror. The focal length of the mirror is -46 cm. Find the location
of the image and the magnification.
1
cm
037
.
0
cm
66
1
cm
46
1
1
1
1 −
−
=
−
−
=
−
=
i
i d
f
d
cm
27
−
=
i
d
( ) 41
.
0
cm
66
cm
27
=
−
−
=
−
=
o
i
d
d
m
36. 25.6 The Mirror Equation and Magnification
Summary of Sign Conventions for Spherical Mirrors
mirror.
concave
a
for
is +
f
mirror.
convex
a
for
is −
f
mirror.
the
of
front
in
is
object
the
if
is +
o
d
mirror.
the
behind
is
object
the
if
is −
o
d
image).
(real
mirror
the
of
front
in
is
object
the
if
is +
i
d
image).
(virtual
mirror
the
behind
is
object
the
if
is −
i
d
object.
upright
an
for
is +
m
object.
inverted
an
for
is −
m
37. 26.1TheIndexof Refraction
s
m
10
00
.
3 8
=
c
Light travels through a vacuum at a speed
Light travels through materials at a speed less than its speed
in a vacuum.
DEFINITION OF THE INDEX OF REFRACTION
The index of refraction of a material is the ratio of the speed
of light in a vacuum to the speed of light in the material:
v
c
n =
=
material
in the
light
of
Speed
in vacuum
light
of
Speed
39. 26.2Snell’sLawandtheRefractionof Light
SNELL’S LAW OF REFRACTION
When light travels from a material
with one index of refraction to a
material with a different index of
refraction, the angle of incidence is
related to the angle of refraction by
2
2
1
1 sin
sin
n
n =
SNELL’S LAW
40. 26.2Snell’sLawandtheRefractionof Light
Example 1 Determining the Angle
of Refraction
A light ray strikes an air/water surface at an
angle of 46 degrees with respect to the
normal. Find the angle of refraction when
the direction of the ray is (a) from air to
water and (b) from water to air.
41. 26.2Snell’sLawandtheRefractionof Light
( ) 54
.
0
33
.
1
46
sin
00
.
1
sin
sin
2
1
1
2 =
=
=
n
n
(a)
(b)
33
2 =
( ) 96
.
0
00
.
1
46
sin
33
.
1
sin
sin
2
1
1
2 =
=
=
n
n
74
2 =
45. 26.2Snell’sLawandtheRefractionof Light
Conceptual Example 4 On the Inside Looking Out
A swimmer is under water and looking up at the surface. Someone
holds a coin in the air, directly above the swimmer’s eyes. To the
swimmer, the coin appears to be at a certain height above the
water. Is the apparent height of the coin greater, less than, or the
same as its actual height?
46. 26.3TotalInternalReflection
When light passes from a medium of larger refractive index into one
of smaller refractive index, the refracted ray bends away from the
normal.
Critical angle 2
1
1
2
sin n
n
n
n
c
=
47. 26.3TotalInternalReflection
Example 5 Total Internal Reflection
A beam of light is propagating through diamond and strikes the diamond-air
interface at an angle of incidence of 28 degrees. (a) Will part of the beam
enter the air or will there be total internal reflection? (b) Repeat part (a)
assuming that the diamond is surrounded by water.
49. 26.3TotalInternalReflection
Conceptual Example 6 The Sparkle of a Diamond
The diamond is famous for its sparkle because the light coming from
it glitters as the diamond is moved about. Why does a diamond
exhibit such brilliance? Why does it lose much of its brilliance when
placed under water?
55. 26.6Lenses
Lenses refract light in such a way that an image of the light source is
formed.
With a converging lens, paraxial rays that are parallel to the principal
axis converge to the focal point.
56. 26.6Lenses
With a diverging lens, paraxial rays that are parallel to the principal
axis appear to originate from the focal point.
59. 26.7TheFormationofImagesbyLenses
IMAGE FORMATION BY A CONVERGING LENS
In this example, when the object is placed further than
twice the focal length from the lens, the real image is
inverted and smaller than the object.
64. 26.8TheThin-LensEquationandtheMagnificationEquation
Summary of Sign Conventions for Lenses
lens.
converging
a
for
is +
f
lens.
diverging
a
for
is −
f
lens.
the
of
left
the
to
is
object
the
if
is +
o
d
lens.
the
of
right
the
to
is
object
the
if
is −
o
d
image).
(real
lens
the
of
right
the
to
formed
image
an
for
is +
i
d
image).
(virtual
lens
the
of
left
the
to
formed
image
an
for
is −
i
d
image.
upright
an
for
is +
m
image.
inverted
an
for
is −
m
65. 26.8TheThin-LensEquationandtheMagnificationEquation
Example 9 The Real Image Formed by a Camera Lens
A 1.70-m tall person is standing 2.50 m in front of a camera. The
camera uses a converging lens whose focal length is 0.0500 m.
(a)Find the image distance and determine whether the image is
real or virtual. (b) Find the magnification and height of the image
on the film.
1
m
6
.
19
m
50
.
2
1
m
0500
.
0
1
1
1
1 −
=
−
=
−
=
o
i d
f
d
(a)
m
0510
.
0
=
i
d real image
(b) 0204
.
0
m
50
.
2
m
0510
.
0
−
=
−
=
−
=
o
i
d
d
m
( )( ) m
0347
.
0
m
50
.
2
0204
.
0 −
=
−
=
= o
i mh
h
71. 26.10TheHumanEye
Example 12 Eyeglasses for the Nearsighted Person
A nearsighted person has a far point located only 521 cm from the
eye. Assuming that eyeglasses are to be worn 2 cm in front of the
eye, find the focal length needed for the diverging lens of the glasses
so the person can see distant objects.
74. 26.10TheHumanEye
THE REFRACTIVE POWER OF A LENS – THE DIOPTER
( )
meters
in
1
diopters)
(in
power
Refractive
f
=
Optometrists who prescribe correctional lenses and the opticians
who make the lenses do not specify the focal length. Instead
they use the concept of refractive power.
75. 29.1WaveParticleDuality
When a beam of electrons is used in a
Young’s double slit experiment, a fringe
pattern occurs, indicating interference
effects.
Waves can exhibit particle-like
characteristics, and particles can exhibit
wave-like characteristics.
76. 29.3PhotonsandthePhotoelectricEffect
Electromagnetic waves are composed of particle-like
entities called photons.
hf
E =
Max Planck
- discovered that the energy of light has an integer
multiple of hf in 1900.
- won the Nobel Prize for this and opened the era of
quantum mechanics.
- Planck’s constant h is also named after him.
Einstein
- found out that not only energy, but light(photons) are
sparse particles.
- won the Nobel Prize for this achievement.
77. 29.2BlackbodyRadiationandPlanck’sConstant
All bodies, no matter how hot or cold,
continuously radiate electromagnetic
waves.
Electromagnetic energy is
quantized.
,
3
,
2
,
1
,
0
=
= n
nhf
E
s
J
10
626
.
6 34
= −
h
Planck’s
constant
frequency
78. What are you observations???
https://www.vascak.cz/data/android/physicsatschool/template.php?s=opt_fotoefekt&l=en
83. 29.3PhotonsandthePhotoelectricEffect
When light shines on a metal, a photon can give
up its energy to an electron in that metal. The
minimum energy required to remove the least
strongly held electrons is called the work
function.
electron
eject
to
needed
work
Minimum
electron
ejected
of
energy
kinetic
Maximum
max
energy
Photon
KE o
W
hf +
=
85. Kinetic Energy of Ejected Electrons
https://javalab.org/en/photoelectric_effect_en/
86. 29.3PhotonsandthePhotoelectricEffect
Example 2 The Photoelectric Effect for a Silver Surface
The work function for a silver surface is 4.73 eV. Find the minimum
frequency that light must have to eject electrons from the surface.
o
o W
hf +
=
=
J
0
max
KE
( )( ) Hz
10
14
.
1
s
J
10
6.626
eV
J
10
60
.
1
eV
73
.
4 15
34
19
=
=
= −
−
h
W
f o
o
87. 29.3PhotoelectricEffect
Most commercially available
silicon solar cells can convert 15
to 25 % of the energy in sunlight.
- basic concept of solar
power generation
Solar cells are made by adding tiny
amounts of phosphorus and boron
to each side of thin silicon plates,
which are commonly used as
semiconductors.
