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Chapter 19: Models of Light

Particle Model of Light – Isaac Newton, in the mid 1600’s

Wave Model of Light – mid to late 1800’s – lots of people – Huygens

Wave-Particle Model – early 1900’s – combines the two ideas

Our understanding of light is still incomplete – neither “wave” nor “particle” is correct – we lack the vocabulary to fully describe light properly

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Wave Refraction and Reflection

In the wave model of light, all parts of a light beam are “interconnected”

For reflection, the speed of the wave does not change after reflection from the boundary. For transmission, the wave front is bent at the interface because (as shown) the wave travels more slowly in the second medium (in this case).

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Particle vs Wave for RefractionA particle of light is incident on the

boundary between two media. i

r

Huygens Principle is an alternate explanation and predicts a slower speed in second medium

Huygens Explanation:

For transmission, the wave front is bent at the interface because (as shown) the wave travels more slowly in the second medium

Particle theory predicts greater speed in 2nd medium

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Speed of Light in a Medium

• We know that light travels at 300,000 km/s in vacuum.

• In any other medium, it travels SLOWER.

• We describe this phenomenon in terms of the INDEX OF REFRACTION of the medium:

• Air: 1.000, Water: 1.33

• Glass: 1.5, Diamond: 2.417

• Cubic Zirconia: 2.21

v

cn

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Snell’s Law of Refraction

i i

r

Speed = v1

Speed = v2

Index of Refraction:

n = c / v

=n1 sin(i) n2 sin(r)

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nwater = 1.33

nair = 1.00

Special Case – Total Internal Reflection

Light bends toward the normal as it passes from one medium into another more optically dense medium.

The reverse is true as well, light bends away from the normal as it passes from a more dense to less dense medium.In such cases there is an angle of incidence for which the angle of refraction is 90o.

This is known as the Critical Angle

c

r=90sin1 / sin2 = n2/ n1

sinc / 1 = 1.00/ 1.33

c = 48.75o

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Total Internal Reflection - Applications

Diamond: n = 2.419Critical Angle = 24.42 degrees

Almost all light entering top face is reflected back inside!!!

Optical Fibres forTransmission of Light

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How a Prism Works

Longer Wavelengths (i.e Red)have smaller index of refractionthan shorter (i.e. Blue).

Smaller index of refraction meansit refracts LESS

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Rainbows!!!

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Light as a Transverse WaveDuring the 1800's there was growing evidence that light may indeed be a wave

phenomena contrary to the beliefs of Isaac Newton.

One piece of evidence was supplied by Thomas Young who showed that light demonstrated the wave property of interference.

http://www.colorado.edu/physics/2000/schroedinger/two-slit2.html

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Polarization of Light

During the 1800's and possibly even during Newton's time there was evidence that particular materials, such as iceland spar, could polarize a ray of light.

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How to polarize light

By absorption

By preferred transmission and reflection

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Applications of PolarizationApplications of Polarization• Astronomy: studying the polarization state of light from stars,

galaxies, nebulae etc. can be used to map magnetic fields either around stars, or within the sun.

• Quantum theory: Many of the foundational problems in quantum theory can be studied using polarized light, e.g. The EPR paradox.

• Chemistry and biology: We've seen how different materials can affect polarized light. Thus, studying these effects can yield a large amount of information about molecular and atomic structure.

• Commercial applications: e.g. Liquid crystals: • Birefringent molecules which can easily be re-oriented due to

the application of an electric field.• Twisted nematic cell. Used for amplitude modulation.• This is the type of liquid crystal most commonly seen in

watches, calculators, LCTVs etc.

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Summary

• Light exhibits both particle-like and wave-like properties

• Light can travel in a vacuum (particle)• Light travels slower in a medium than in vacuum

(mostly wave)• Light reflects (both)• Light refracts (mostly wave)• Light interferes (wave)• Light is polarizable (wave)

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Converging and Diverging Lenses

For the convex lens shown, any parallel rays of light that enter the lens will pass through the focus on the right (f is positive).

c cf f

For a concave lens parallel rays diverge and appear to come from the focus behind the lens (f is negative)

c cf f

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Convex Lenses

Three principle rays can be drawn.1. Ray passes through geometric center of lens

undisturbed2. Parallel ray entering passes through focus3. Ray passes through focus emerges parallel

c cf f

do

di

ho

hi

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Thin Lens Formula

io ddf

111

c cf f

do

di

ho

hi

Magnification Formula:Lens Formula:

i

o

i

o

h

h

d

dm

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Thin Lens Formula

0

0

0

i

o

d

d

f

c cf f

do

di

ho

hi

Object Side Image Side

0

0

0

i

o

d

d

f

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Sample Convex Lens

An 30 cm object is placed 60 cm in front of a convex lens with a focal length of 24 cm . Describe the image.

ho=30

60

hi

di

1/f = 1/do + 1/di 1/24 = 1/60 + 1/di

10/240 = 4/240 + 1/di 1/di = 6/240 di = 40

m = -di/do = -40/60 = - .67 Object is real, smaller (20 cm), and inverted

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Concave Lens ExampleAn object is place 60 cm in front of a concave lens with a focal length of 12 cm . Describe

the image.1/f = 1/do + 1/di -1/12 = 1/60 + 1/di

-5/60 = 1/60 + 1/di 1/di = -6/60 di = -10 (neg sign indicates virtual image)

m = -di/do = - -10/60 = 0.167 Object is virtual, smaller, and upright

ho=30

60

hi

di