chapter 35 the nature of light and the laws of geometric...
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Chapter 35 The Nature of Light and
the Laws of Geometric Optics
35.1 The Nature of Light A dual nature:
1. ParticleNature – Newton’s Particle Model
Albert Einstein (1905)
2. Wave Nature – Huygen (1678), Thomas Young (1801)
Maxwell (18XX)
The energy of a light wave is present in particles called photons and the energy of a
photon is νhE = , where 3410626.6 −×=h (J s) is called Plank’s constant.
Particle --> A photon with frequency f and wavelength λ has energy E,
λhc
hfE == .
Plank’s constant: 3410626.6 −×=h J s, π2h=h
Wave nature: propagation of light
Particle nature: exchange of energy between light and matter
35.2 Measurements of The Speed of
Light Armand Fizeau (1849):
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Michelson’s Method:
458,792,299=c m/s
Example: In Fizeau’s experiment, his wheel had 720 teeth, and light was observed
when the wheel rotated at 25.2 revolutions per second. If the distance from the wheel
to the distant mirror was 8.63 km, what was Fizeau’s value for the speed of light?
720
1
2.25
1=∆t s, ( ) 8
3
1013.3
7202.25
11063.82 ×=
×
×=c
35.3 The Ray
Approximation
Ray approximation: d<<λ (particle nature)
Diffraction: d~λ (wave nature)
a) d<<λ , ray, particle
b) d~λ , diffraction, wave
c) d>>λ , point source
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35.4 The Wave Under Reflection
Physical Mechanisms for Reflection and Refraction
absorption and re-radiation of the light by the atoms
Specular Reflection and Diffuse Reflection
specular reflection: reflection from a smooth surface
diffuse reflection: the surface reflects the rays not as a parallel set
Law of reflection:
'11 θθ =
35.5 The Wave Under Refraction The light propagates slower in medium.
index of refraction: v
cn =
glass: 66.150.1 −=n
substance (solid) n substance (fluid) n
Diamond 2.419 Benzene 1.501
Fused Quartz (SiO2) 1.458 Water 1.333
Ics 1.309 air 1.000293
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NaCl 1.544 CO2 1.0045
Example: The speed of light in silica. (a) Find the speed of light in silica. (quartz
SiO2)
Law of refraction (Snell’s law):
2211 sinsin θθ nn =
Example: Light passing through a slab
If the thickness of the slab is h, calculate d.
( ) ( )
( )
−
−=−=
−=−=
2
12
1
12
1
11211
21212
212
sin1
sin
cossintancossin
sincoscossincos
sincos
θ
θθθθθθ
θθθθθ
θθθ
n
n
n
n
hh
hhd
Example: Measuring n Using a Prism
35.6 Huygens’s Principle Each point on a primary wavefront serves as the sources of spherical secondary
wavelets that advance with a speed and frequency equal to those of the primary wave.
The primary wavefront at some later time is the envelope of these wavelets.
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Reflection:
11 θθ =
Refraction:
tv
tv
2
1
2
1
sinsin =
θθ
Fermat’s Principle
Fermat’s principle for refraction
( )
2
22
1
22
22
v
axd
v
ax
t
+−+
+=
0=∂∂x
t
2
1
2
1
sin
sin
v
v=
θθ
index of refraction: v
cn = ,
2
1
1
2
2
1
2
1
sin
sin
/
/
θθ
===n
n
nc
nc
v
v
35.7 Dispersion
Dispersion
Velocities of light with different colors vary in medium (not in
vacuum). The variance of light velocity results in dispersion.
Rainbows Calculating the Angular Radius of the Rainbow
Primary reflection:
d
x
a/2
d-x
[(d-x)2+(a/2)2]1/2
[x2+(a/2)2]1/2 n1
n2
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?=β in terms of 1θ and 2θ , 21 sinsin θθ waterair nn = --> write ( )1θββ =
πβφ =+ 2d
( ) 221 θθθβ =−+ --> 122 θθβ −=
the angles of deviation: ?=dφ
−+=+−=−= −
water
aird n
n 11112
sinsin42242
θθπθθπβπφ
The intensity of the reflected light reaches its maximum at
the angle of minimum deviation.
Material Blue
(486.1 nm)
Yellow
(589.3 nm)
Red
(656.3 nm)
Crown Glass 1.524 1.517 1.515
Flint Glass 1.639 1.627 1.622
Water 1.337 1.333 1.331
Cargille Oil 1.530 1.520 1.516
Carbon Disulfide 1.652 1.628 1.618
Table 2
35.8 Total Internal Reflection ( )Onn 90sinsin 21 =θ --> 21 nn >
Example: A particular glass has an index of refraction of 5.1=n . What is the critical
angle for total reflection for light leaving this glass and entering air, for which
n1
n2
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0.1=n ?
OC 90sin0.1sin5.1 =θ
Example: While under the water, you look up and
notice that you see objects above water level in a
circle of light of radius approximately 2.0 m, and the
rest of your vision is the color of the sides of the pool.
How deep are you in the pool?
oc 90sin0.1sin33.1 =θ , cy
R θtan= --> y = ?
Optical Fibers
Mirages
n1
n2