30. Reflection & Refraction

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Topics

The Speed of Light

Reflection, Refraction

Polarization Revisited

Spectroscopy

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Speed of Light

The first hint that lighttraveled at a finite speed came from measurements of the period of Jupiter’s moon Io

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Speed of Light

Ole Rømer’s Method (1675)(Römer, Roemer)

When the Earth was at point Cthe eclipses of Io were observed to be later than predicted by about 16.6 minutes

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Speed of Light

Rømer’s Method (1675)

Rømer reasoned that this mustbe due to the time it takeslight to traverse the diameterof the Earth’s orbit

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Speed of Light

Today, the speed of light is defined to beexactly

c = 299792458 m/s

The meter is now defined to be thedistance traveled by light in vacuum in

1/299792458 s

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Speed of Light

Distances in astronomy are so great thatit is customary to use the distance traveledby light in a given time as a unit of distanceExamples – distance from Earth to:

1. Moon 1.25 light-seconds2. Sun 8.33 light-minutes3. Pluto 5.5 light-hours4. Alpha Centauri 4.5 light-years (ly)5. Andromeda 2.1 million ly

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Fermat’s Principle

Light travels from one point to another along the path of least time

Note: The path of least time is notnecessarily the shortest path

Reflection & Refraction

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Reflection & Refraction

The speed of light v in a transparentmedium is less than its speed c in vacuum. Such media are characterizedby an index of refraction, n

cn

v

For water n = 1.33For glass n = 1.5 to 1.66

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Frequency Between Media

As light travels from one medium to another, its frequency does not change But the wave speed and the

wavelength do change The wave fronts do not pile up at

the boundary, so the ƒrequency must stay the same

v f

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Reflection & Refraction

Law of Reflection: angle of reflection = angle of incidence

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Reflection & Refraction

Snell’s Law of Refraction(Willebrord Snel van Royen, 1621)

1 1 2 2sin sinn n

Angle ofrefraction

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Example: Refraction from Air to Water

2 2 1 1

1 12 1

2

0

sin sin

sin sin

32.1

n n

n

n

Air: n1 = 1Water: n2 = 1.331 = 45o

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Reflection & Refraction

As the angle of incidence is increased a critical angle of incidence c is reached at whichthe angle of refraction is 90o.

01 1 2

2c

1

sin sin 90

sin

n n

n

n

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Total internal Reflection

If the angle of incidence is is greater than the critical angle c there is no refracted ray. All the light is reflected. This is called total internal reflection.This requires n1 > n2

1

2sin c

n

n

Examples of Reflection and Refraction

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Light can be transmitted along transparentglass fibers using total internal reflection. Such fibers are used in imaging and form the backbone of the internet and othertelecommunications

Fiber Optics

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Mirages

These are caused by a continuous changein the index of refraction of a medium,which leads to the gradual bending of light

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Dispersion

The index of refraction depends slightlyon the wavelength. This causes lightcomprising an admixture of wavelengths, e.g., white light, to be dispersed intothe different wavelengthcomponents

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Index of Refraction versus Wavelength

The index of refraction for a material usually decreases with increasing wavelength

Violet light refracts more than red light when passing from air into a denser material

That’s Why the Sky is Blue!

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The parish of Soufrière, Dominica

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Rainbows

Reflection inside rain drop at the back surface

Followed by refraction on leaving rain drop

Net angle of deviation depends on color:violet deviates by 40°red deviates by 42°

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Rainbows

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Rainbows

Red appears on the outermost ring of rainbow, while violet appears on the innermost ring.

Polarization Revisited

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Polarization

Polarization by AbsorptionA polarizer is a device that allows onlywaves of a given polarization through.

y

xz

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Polarization

Polarization by ReflectionElectromagnetic radiation cannot be emitted in direction of the oscillating electric field, sothere is no reflected ray when

tanp = n2/n1

y

xz

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Spectroscopy

Hydrogen

Helium

Barium

Mercury

Continuousspectrum

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Summary Speed of light in vacuum

299792458 m/s (by definition) Reflection and refraction

Occur at media boundaries Snell’s law n1sin1 = n2sin2 Total internal reflection n1sinc = n2 Dispersion

n varies with wavelength Polarization

by absorption and reflection