How is Light Made? How is Light Made? Deducing Temperatures and - PDF document

How is Light Made? How is Light Made? Deducing Temperatures and Deducing Temperatures and Luminosities of Stars Luminosities of Stars (and other objects… …) ) (and other objects 1

Review: Electromagnetic (EM) Radiation Review: Electromagnetic (EM) Radiation • EM radiation: regularly varying electric & magnetic fields – can transport energy over vast distances. • “Wave-Particle Duality” of EM radiation: – Can be considered as EITHER particles ( photons ) or as waves • Depends on how it is measured • Includes all of “classes” of light – ONLY distinction between X-rays and radio waves is wavelength λ Increasing energy ) V s s U t ) s e y h R e ( v a g I v t ( a R e i a L d w l s w o e a y e o m i r o l a v b a r i a d m R i r c r s f a i n a X t M i R l V I G U 10 -15 m 10 3 m 10 -9 m 10 -6 m 10 -4 m 10 -2 m Increasing wavelength Electromagnetic radiation is everywhere around us. It is the light that we see, it is the heat that we feel, it is the UV rays that gives us sunburn, and it is the radio waves that transmit signals for radio and TVs. EM radiation can propagate through vacuum since it doesn’t need any medium to travel in, unlike sound. The speed of light through vacuum is constant through out the universe, and is measured at 3x10 8 meters per second, fast enough to circle around the earth 7.5 times in 1 second. Its properties demonstrate both wave-like nature (like interference) and particle-like nature (like photo-electric effect.) 2

Electromagnetic Fields Electromagnetic Fields Direction of “Travel” 3

Sinusoidal Fields Sinusoidal Fields • BOTH the electric field E and the magnetic field B have “sinusoidal” shape 4

λ Wavelength λ Wavelength λ � Distance between two identical points on wave One way of describing light is by its wavelength. Wavelength is the distance between the two identical points on the wave. The wave must be steady (no change in the oscillation and no change in its velocity) for it be possible to measure the wavelength. Wavelength is also shorthanded to a Greek letter Lambda. 5

ν Frequency ν Frequency time 1 unit of time (e.g., 1 second) � number of wave cycles per unit time registered at given point in space � inversely proportional to wavelength The same exact wave can be described using its frequency. Frequency is defined as the number of cycles of the waves per unit time. In the case shown, the frequency would be 1.5, since there are exactly one and a half complete cycles of the wave in the given time. The frequency is inversely proportional to its wavelength. Frequency is denoted by Greek letter “nu”. 6

Wavelength and Frequency Wavelength and Frequency λ = v /ν = c /ν (in vacuum) � Proportional to Velocity v � Inversely proportional to temporal frequency ν � Example: � AM radio wave at ν = 1000 kHz = 10 6 Hz � λ = c/ ν = 3 × 10 8 m/s / 10 6 Hz = 300 m � λ for AM radio is long because frequency is small Wavelength and frequency are related to one another by the wave’s velocity. Wavelength is proportional (wavelength increases if velocity increases), and wavelength is inversely proportional to frequency (wavelength decreases if frequency increases). An AM radio wave has a large wavelength, so it has a low frequency (compared to other EM radiation.) In the case of EM radiation, the velocity is the speed of light, denoted by c. the speed of light is as mentioned before, approximately 3x10 8 meters per second. Using algebra, one can solve for any one of the variables. 7

“Units Units” ” of Frequency of Frequency “ ⎡ ⎤ meters c ⎢ ⎥ ⎡ ⎤ ⎣ ⎦ = cycles second ν ⎢ ⎥ ⎡ ⎤ ⎣ ⎦ second meters λ ⎢ ⎥ ⎣ ⎦ cycle ⎡ ⎤ = cycle 1 1 "Hertz" (Hz) ⎢ ⎥ ⎣ ⎦ second 8

Light as a Particle: Photons Light as a Particle: Photons � Photons: little “packets” of energy � Energy is proportional to frequency E = h ν Energy = (Planck’s constant) × (frequency of photon) h ≈ 6.625 × 10 -34 Joule-seconds = 6.625 × 10 -27 Erg-seconds Now the particle nature of EM radiation. These little packets of light is known as photons. These photons carry a certain energy which is related to its frequency. This energy is equal to Planck’s constant (h) multiplied by the frequency of the photon. By substituting “nu” with the equation in the previous slide, we can get the equivalent equation in terms of wavelength. Planck’s constant is 6.6261 x 10-34 joule second 9

Generating Light Generating Light • Light is generated by converting one class of energy to electromagnetic energy – Heat – Explosions 10

Converting Heat to Light Converting Heat to Light The Planck Function The Planck Function • Every opaque object (a human, a planet, a star) radiates a characteristic spectrum of EM radiation – Spectrum: Distribution of intensity as function of wavelength – Distribution depends only on object’s temperature T • Blackbody radiation ultraviolet visible infrared radio Intensity (W/m 2 ) 0.1 1.0 10 100 1000 10000 11

Planck’ ’s Radiation Law s Radiation Law Planck • Wavelength of MAXIMUM emission λ max is characteristic of temperature T • Wavelength λ max ↓ as T ↑ As T ↑ , λ max ↓ λ max http://scienceworld.wolfram.com/physics/PlanckLaw.html 12

Sidebar: The Actual Equation Sidebar: The Actual Equation 2 2 1 hc ( ) = B T λ 5 hc − e λ kT 1 • Derived in Solid State Physics • Complicated!!!! (and you don’t need to know it!) h = Planck’s constant = 6.63 × 10 -34 Joule - seconds k = Boltzmann’s constant = 1.38 × 10 -23 Joules per Kelvin c = velocity of light = 3 × 10 +8 meter - second -1 13

Temperature dependence Temperature dependence of blackbody radiation of blackbody radiation • As object’s temperature T increases : 1. Wavelength of maximum of blackbody spectrum (Planck function) becomes shorter (photons have higher energies) 2. Each unit surface area of object emits more energy (more photons) at all wavelengths 14

Shape of Planck Curve Shape of Planck Curve http://csep10.phys.utk.edu/guidry/java/planck/planck.html • “Normalized” Planck curve for T = 5700K – Maximum Intensity set to 1 • Note that maximum intensity occurs in visible region of spectrum for T = 5700K 16

Planck Curve for T = 7000- -K K Planck Curve for T = 7000 http://csep10.phys.utk.edu/guidry/java/planck/planck.html • This graph is also “normalized” to 1 at maximum • Maximum intensity occurs at shorter wavelength λ – boundary of ultraviolet (UV) and visible 17

Two Planck Functions Two Planck Functions Displayed on Logarithmic Scale Displayed on Logarithmic Scale http://csep10.phys.utk.edu/guidry/java/planck/planck.html • Graphs for T = 5700K and 7000K displayed on same logarithmic scale without normalizing – Note that curve for T = 7000K is “higher” and its peak is farther “to the left” 18

Features of Graph of Planck Law Features of Graph of Planck Law T 1 < T 2 T 1 < T (e.g., T 1 = 5700K, T 2 = 7000K) 2 (e.g., T 1 = 5700K, T 2 = 7000K) • Maximum of curve for higher temperature occurs at SHORTER wavelength λ : – λ max (T = T 1 ) > λ max (T = T 2 ) if T 1 < T 2 • Curve for higher temperature is higher at ALL WAVELENGTHS λ ⇒ More light emitted at all λ if T is larger – Not apparent from normalized curves, must examine “unnormalized” curves, usually on logarithmic scale 19

Wavelength of Maximum Emission Wavelength of Maximum Emission Wien’ ’s s Displacement Law Displacement Law Wien • Obtained by evaluating derivative of Planck Law over temperature T − × 3 2.898 10 [ ] λ = meters [ ] max K T Human vision range 400 nm = 0.4 µ m ≤ λ ≤ 700 nm = 0.7 µ m (1 µ m = 10 -6 m) 20

Colors of Stars Colors of Stars • Star “Color” is related to temperature – If star’s temperature is T = 5000K, the wavelength of the maximum of the spectrum is: − × 3 2 . 898 10 λ = ≅ µ = m 0 . 579 m 579 nm max 5000 (in the visible region of the spectrum, green) 21

Colors of Stars Colors of Stars • If T << 5000 K (say, 2000 K), the wavelength of the maximum of the spectrum is: × − 3 2 . 898 10 λ = ≅ µ ≅ m 0 . 966 m 966 nm max 3000 (in the “near infrared” region of the spectrum) • The visible light from this star appears “reddish” – Why? 22

Blackbody Curve for T=3000K Blackbody Curve for T=3000K • In visible region, more light at long λ ⇒ Visible light from star with T=3000K appears “reddish” 23

Colors of Stars Colors of Stars • If T << 5000 K (say, 2000 K), the wavelength of the maximum of the spectrum is: − × 3 2 . 898 10 λ = ≅ µ ≅ m 1 . 449 m 1450 nm max 2000 (peaks in the “near infrared” region of the spectrum) 24

Colors of Stars Colors of Stars • Color of star indicates its temperature – If star is much cooler than 5,000K, the maximum of its spectrum is in the infrared and the star looks “reddish” • It gives off more red light than blue light – If star is much hotter than 15,000K, its spectrum peaks in the UV, and it looks “bluish” • It gives off more blue light than red light 25