Waves and LightWaves and Light

• A wave is a pattern that moves.A wave is a pattern that moves.

• As the pattern moves, the medium As the pattern moves, the medium may “jiggle”, but on average it stays may “jiggle”, but on average it stays put.put.

• Example: Wave on a string, string Example: Wave on a string, string bobs up and down but does not move bobs up and down but does not move along with wave.along with wave.

• We usually think of periodic waves, but We usually think of periodic waves, but pulses are also waves.pulses are also waves.

Periodic WavesPeriodic Waves

• Wavelength (Wavelength () = distance between peaks.) = distance between peaks.

• Frequency (Frequency (f f ) = number of peaks that pass ) = number of peaks that pass by a point per second.by a point per second.

• Amplitude = ½ of peak to trough “distance”Amplitude = ½ of peak to trough “distance”

•We will often talk about the period of the wave T=1/f . . The Period is the time interval between peaks.

•Example: If the frequency of a wave is 20s-1 = 20 Hz, this means that 20 peaks pass by per second. Thus, the period of the wave is 1/20 s.

Period and FrequencyPeriod and Frequency

Wavelength and Wave Wavelength and Wave numbernumber

• We sometimes refer to the waves We sometimes refer to the waves number k=1/number k=1/ = number of waves = number of waves per unit length.per unit length.

• Very useful in some advanced Very useful in some advanced methodologies, but we will not use it methodologies, but we will not use it very much.very much.

• A given type of wave (e.g. sound, light) A given type of wave (e.g. sound, light) moves at a constant velocity that is moves at a constant velocity that is determined by the medium that supports the determined by the medium that supports the wave. (different speeds for different media)wave. (different speeds for different media)

• Speed of sound in air is cSpeed of sound in air is css=340 m/s (on a =340 m/s (on a typical day)typical day)

• Speed of light in a vacuum is c=3Speed of light in a vacuum is c=3101088m/s.m/s.

• Wavelength, frequency and speed are related Wavelength, frequency and speed are related by the equationby the equation

c=c=f f

Wave Speed (c) Wave Speed (c)

Longitudinal and Transverse Longitudinal and Transverse WavesWaves

• Transverse Wave: Transverse Wave: Wave Motion Wave Motion (disturbance) is (disturbance) is perpendicular to perpendicular to direction of direction of propagation of propagation of wave.wave.

• Example: water Example: water waves, lightwaves, light

• Longitudinal/Longitudinal/Compressional Compressional waves: waves: distrurbance is distrurbance is parallel to direction parallel to direction of propagation. of propagation.

• Example: sound Example: sound waves in air and waves in air and waterwater

Difference between compressional and Difference between compressional and transverse waves allows us to “see” into the transverse waves allows us to “see” into the earthearth

Principle of SuperpositionPrinciple of Superposition• Waves obey the principle of superposition: When Waves obey the principle of superposition: When

two or more waves are present in the same two or more waves are present in the same location, the net amplitude is just the sum of the location, the net amplitude is just the sum of the individual amplitudes. Result is complex wave individual amplitudes. Result is complex wave formsforms

Electromagnetic WavesElectromagnetic Waves• All electromagnetic waves travel at in All electromagnetic waves travel at in

vacuum at the speed of light, vacuum at the speed of light, c=3c=3101088m/sm/s

• Since c=Since c=f f , , we know that frequency we know that frequency is inversely proportional to is inversely proportional to wavelength.wavelength.

• ““They” used to believe that light They” used to believe that light needed a medium to travel in. needed a medium to travel in.

• When Traveling through mater, When Traveling through mater, different wavelength behave different wavelength behave differently.differently.

• Examples, X-rays pass right through Examples, X-rays pass right through solid objects but visible light does solid objects but visible light does not.not.

• Infrared video.Infrared video.

• We may use all wavelengths to study We may use all wavelengths to study nature. nature.

Milky Way as Seen in Various Milky Way as Seen in Various FrequenciesFrequencies

When discussing a wave, the term When discussing a wave, the term frequency refers tofrequency refers to

1 2 3

31%

4%

64%1.1. The distance The distance

between two between two adjacent peaksadjacent peaks

2.2. The number of The number of peaks that pass a peaks that pass a point per secondpoint per second

3.3. The time interval The time interval between two peaks between two peaks passing a point.passing a point.

List the type of radiation from low List the type of radiation from low frequency to high frequencyfrequency to high frequency

70%

7%

24%

1 2 3

1.1. Infrared, visible, Infrared, visible, ultraviolet, x-ultraviolet, x-ray, ray,

2.2. Infrared, visible Infrared, visible x-ray, ultravioletx-ray, ultraviolet

3.3.x-ray, x-ray, ultraviolet, ultraviolet, visible, infraredvisible, infrared

Infrared radiation can pass Infrared radiation can pass through some materials that block through some materials that block visible light and vice versa.visible light and vice versa.

1 2

7%

93%

1.1.TrueTrue

2.2.FalseFalse

Thermal RadiationThermal Radiation• All objects with non zero temperature All objects with non zero temperature

radiate energy. radiate energy.

Two important pointsTwo important points

• Total radiated energy (area under Total radiated energy (area under curve) is much higher for higher curve) is much higher for higher temperatures.temperatures.

• Peak in radiation spectrum for higher Peak in radiation spectrum for higher temperatures is at shorter temperatures is at shorter wavelengthswavelengths

Two Important EquationsTwo Important Equations

spectrumradiation in peak λ

Where

2900

eTemperaturKelvin T

emissivity (usually) 1e

Area SurfaceA Km

W105.67σ

Where

max

max

428-

4

mKT

eATP

ExampleExample

• Sun T=6000KSun T=6000Kmaxmax=2900=2900mK/6000K=0.483mK/6000K=0.483m m

(Visible)(Visible)

• Earth T=300KEarth T=300Kmaxmax=2900=2900mK/300K=9.66mK/300K=9.66m m

(Infrared)(Infrared)

Total Power Radiated by Total Power Radiated by SunSun

• A=4A=4RRss2 2 = 4 = 4(7(7101088m)m)22 =6.16 =6.1610101818mm22

P=P=eATeAT44

=(5.67=(5.671010-8-8W/mW/m22KK44)(1)(6.16)(1)(6.1610101818mm22)(6000K))(6000K)44

=4.5=4.510102626WW

As a comparison, total electrical power As a comparison, total electrical power generated on earth is 10generated on earth is 101313W. In one W. In one second, the sun generates as much energy second, the sun generates as much energy as all of the power plants on earth do in as all of the power plants on earth do in 1,500,000 years!1,500,000 years!

Line RadiationLine Radiation

• All atoms/molecules also radiate at All atoms/molecules also radiate at discrete frequencies that are discrete frequencies that are determined by their structure.determined by their structure.

• Can use the emitted lines to Can use the emitted lines to determine what atoms/molecules are determine what atoms/molecules are present.present.

• Need to use quantum mechanics to Need to use quantum mechanics to calculate spectrum.calculate spectrum.

Examples of line radiation for various elements

Light spectrum from various Light spectrum from various sourcessources

•Materials also can absorb light at the same frequencies that Materials also can absorb light at the same frequencies that they emit it.they emit it.

•Solar spectrum showing absorption by gasses in outer layerSolar spectrum showing absorption by gasses in outer layer

Solar Spectrum observed on Solar Spectrum observed on earthearth

Wave Properties of lightWave Properties of light

• Reflection: Waves bouncing off of objects.Reflection: Waves bouncing off of objects.Important when objects are larger than the Important when objects are larger than the wavelengthwavelength

• Diffraction: Waves “bending” around Diffraction: Waves “bending” around objects objects Important when objects are about Important when objects are about the same size as the wavelengththe same size as the wavelength

• Refraction: light changing direction when Refraction: light changing direction when it changes mediumit changes mediumImportant at all wavelengthsImportant at all wavelengths

ReflectionReflection

Reflection:Reflection:

ri

RefractionRefraction

Total Internal Reflection

Index of refractionIndex of refraction

• Index of refraction for a material, nIndex of refraction for a material, n

1materialin light of speed

in vacuumlight of speedn

Snell’s Law for RefractionSnell’s Law for Refraction

)sin()sin( 2211 nn If n1>n2 then 1< 2 (bends away from normal)

If n1<n2 then 1> 2 (bends towards normal)

RainbowsRainbows

DiffractionDiffraction

Scattering by particulatesScattering by particulates

• The amount of scattering depends on The amount of scattering depends on the particle size and the frequency of the particle size and the frequency of the light. (Rayleigh scattering )the light. (Rayleigh scattering )

• Small particles scatter blue light Small particles scatter blue light more than red lightmore than red light

Why is the sky blue?Why is the sky blue?

Why are sunsets redWhy are sunsets red

Albedo:Albedo:

Energy Incident

ReflectedEnergy Albedo