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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