Waves and Light

A wave is a pattern that moves. A wave is a pattern that moves. As the pattern moves, the medium may “jiggle”, but on average it stays put. As the pattern moves, the medium may “jiggle”, but on average it stays put. Example: Wave on a string, string bobs up and down but does not move along with wave. Example: Wave on a string, string bobs up and down but does not move along with wave. We usually think of periodic waves, but pulses are also waves. We usually think of periodic waves, but pulses are also waves.

Periodic Waves Wavelength ( ) = distance between peaks. Wavelength ( ) = distance between peaks. Frequency (f ) = number of peaks that pass by a point per second. Frequency (f ) = number of peaks that pass 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 Frequency

Wavelength and Wave number We sometimes refer to the waves number k=1/ = number of waves per unit length. We sometimes refer to the waves number k=1/ = number of waves per unit length. Very useful in some advanced methodologies, but we will not use it very much. Very useful in some advanced methodologies, but we will not use it very much.

A given type of wave (e.g. sound, light) moves at a constant velocity that is determined by the medium that supports the wave. (different speeds for different media) A given type of wave (e.g. sound, light) moves at a constant velocity that is determined by the medium that supports the wave. (different speeds for different media) Speed of sound in air is c s =340 m/s (on a typical day) Speed of sound in air is c s =340 m/s (on a typical day) Speed of light in a vacuum is c=3  10 8 m/s. Speed of light in a vacuum is c=3  10 8 m/s. Wavelength, frequency and speed are related by the equation Wavelength, frequency and speed are related by the equation c= f c= f Wave Speed (c)

Longitudinal and Transverse Waves Transverse Wave: Wave Motion (disturbance) is perpendicular to direction of propagation of wave. Transverse Wave: Wave Motion (disturbance) is perpendicular to direction of propagation of wave. Example: water waves, light Example: water waves, light

Longitudinal/Compres sional waves: distrurbance is parallel to direction of propagation. Longitudinal/Compres sional waves: distrurbance is parallel to direction of propagation. Example: sound waves in air and water Example: sound waves in air and water

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

Principle of Superposition Waves obey the principle of superposition: When two or more waves are present in the same location, the net amplitude is just the sum of the individual amplitudes. Result is complex wave forms Waves obey the principle of superposition: When two or more waves are present in the same location, the net amplitude is just the sum of the individual amplitudes. Result is complex wave forms

Electromagnetic Waves All electromagnetic waves travel at in vacuum at the speed of light, c=3  10 8 m/s All electromagnetic waves travel at in vacuum at the speed of light, c=3  10 8 m/s Since c= f, we know that frequency is inversely proportional to wavelength. Since c= f, we know that frequency is inversely proportional to wavelength. “They” used to believe that light needed a medium to travel in. “They” used to believe that light needed a medium to travel in.

When Traveling through mater, different wavelength behave differently. When Traveling through mater, different wavelength behave differently. Examples, X-rays pass right through solid objects but visible light does not. Examples, X-rays pass right through solid objects but visible light does not. Infrared video. Infrared video. We may use all wavelengths to study nature. We may use all wavelengths to study nature.

Milky Way as Seen in Various Frequencies

When discussing a wave, the term frequency refers to 1. The distance between two adjacent peaks 2. The number of peaks that pass a point per second 3. The time interval between two peaks passing a point.

List the type of radiation from low frequency to high frequency 1. Infrared, visible, ultraviolet, x-ray, 2. Infrared, visible x- ray, ultraviolet 3. x-ray, ultraviolet, visible, infrared

Infrared radiation can pass through some materials that block visible light and vice versa. 1. True 2. False

Thermal Radiation All objects with non zero temperature radiate energy. All objects with non zero temperature radiate energy.

Two important points Total radiated energy (area under curve) is much higher for higher temperatures. Total radiated energy (area under curve) is much higher for higher temperatures. Peak in radiation spectrum for higher temperatures is at shorter wavelengths Peak in radiation spectrum for higher temperatures is at shorter wavelengths

Two Important Equations

Example Sun T=6000K Sun T=6000K max =2900  mK/6000K=0.483  m (Visible) max =2900  mK/6000K=0.483  m (Visible) Earth T=300K Earth T=300K max =2900  mK/300K=9.66  m (Infrared) max =2900  mK/300K=9.66  m (Infrared)

Total Power Radiated by Sun A=4  R s 2 = 4  (7  10 8 m) 2 =6.16  m 2 A=4  R s 2 = 4  (7  10 8 m) 2 =6.16  m 2 P=  eAT 4 =(5.67  W/m 2 K 4 )(1)(6.16  m 2 )(6000K) 4 =(5.67  W/m 2 K 4 )(1)(6.16  m 2 )(6000K) 4 =4.5  W =4.5  W As a comparison, total electrical power generated on earth is W. In one second, the sun generates as much energy as all of the power plants on earth do in 1,500,000 years!

Line Radiation All atoms/molecules also radiate at discrete frequencies that are determined by their structure. All atoms/molecules also radiate at discrete frequencies that are determined by their structure. Can use the emitted lines to determine what atoms/molecules are present. Can use the emitted lines to determine what atoms/molecules are present. Need to use quantum mechanics to calculate spectrum. Need to use quantum mechanics to calculate spectrum.

Examples of line radiation for various elements

Light spectrum from various sources

Materials also can absorb light at the same frequencies that they emit it. Materials also can absorb light at the same frequencies that they emit it. Solar spectrum showing absorption by gasses in outer layer Solar spectrum showing absorption by gasses in outer layer

Solar Spectrum observed on earth

Wave Properties of light Reflection: Waves bouncing off of objects. Reflection: Waves bouncing off of objects. Important when objects are larger than the wavelength Diffraction: Waves “bending” around objects Important when objects are about the same size as the wavelength Diffraction: Waves “bending” around objects Important when objects are about the same size as the wavelength Refraction: light changing direction when it changes medium Refraction: light changing direction when it changes medium Important at all wavelengths

Reflection

Reflection:

Refraction Total Internal Reflection

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

Snell’s Law for Refraction If n 1 >n 2 then  1 <  2 (bends away from normal) If n 1  2 (bends towards normal)

Rainbows

Diffraction

Scattering by particulates The amount of scattering depends on the particle size and the frequency of the light. (Rayleigh scattering ) The amount of scattering depends on the particle size and the frequency of the light. (Rayleigh scattering ) Small particles scatter blue light more than red light Small particles scatter blue light more than red light

Why is the sky blue?

Why are sunsets red

Albedo: