Today. Electromagnetic Radiation. Light & beyond. Thermal Radiation. Wien & Stefan-Boltzmann Laws

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1 Today Electromagnetic Radiation Light & beyond Thermal Radiation Wien & Stefan-Boltzmann Laws 1

2 Electromagnetic Radiation aka Light Properties of Light are simultaneously wave-like AND particle-like Sometimes it behaves like ripples on a pond (waves). Sometimes it behaves like billiard balls (particles). Called the wave-particle duality in quantum mechanics. 2

3 Particles of Light Particles of light are called photons. Each photon has a wavelength and a frequency. The energy of a photon depends on its frequency. 3

4 Wavelength and Frequency 4

5 Wavelength & Frequency λ = wavelength (separation between crests) f = frequency (rate of oscillation) c = speed of light = m/s λf = c 5

6 Wavelength, Frequency, and Energy photon energy: E = hf = hc/λ h = joule s (Planck s constant) 6

7 N1-05 E, f increasing λ decreasing 7

8 Same stuff, different Energy: Radio microwave infrared visible light ultraviolet X-ray gamma ray Energy per photon increasing 8

9 How do light and matter interact? Emission Absorption Transmission: Transparent objects transmit light. Opaque objects block (absorb) light. Reflection or scattering 9

10 Earth s atmosphere is opaque to light at most wavelengths. It is transparent only to visible light and radio waves. 10

11 Reflection and Scattering Mirror reflects light in a particular direction. Movie screen scatters light in all directions. 11

12 We see by scattered light Interactions between light and matter determine the appearance of everything around us. 12

13 Production of light Why do stars shine? They re hot! 13

14 Thermal Radiation Nearly all large, dense objects emit thermal radiation, including stars, planets, and you. An object s thermal radiation spectrum depends on only one property: its temperature. 14

15 Properties of Thermal Radiation 1. Hotter objects emit more light at all frequencies per unit area. 2. Hotter objects emit photons with a higher average energy. Spectrum: Intensity Wavelength λ 15

16 Wien s Law λpt = 2.9 x 10 6 nm K λp is the wavelength of maximum emission (in nanometers nano = 10-9 ) T is temperature (in degrees Kelvin) As T increases, wavelength decreases. So hot object blue; cool objects red. 16

17 2 Examples: Human body T = 310 K λ p = nm K 310 K =10, 000 nm We radiate in the infrared The Sun T = 5,800 K λ p = nm K 5800 K The sun radiates visible light = 500 nm 17

18 Properties of Thermal Radiation 1. Hotter objects emit photons with a higher average energy. λp 18

19 Stefan-Boltzmann Law L =4πR 2 σt 4 surface area of a sphere L = Luminosity (energy per time radiated) R = Radius (e.g., of a star) T = Temperature (of radiating surface, in K) σ = Stefan-Boltzmann constant just a number to make units work right L R 2 T 4 The absolute brightness of a star depends on its size (R) and temperature (T). 19

20 Using Stefan-Boltzmann Law A.L goes down by a factor 4 B. L stays the same C. L goes up by a factor 4 D.L goes up by a factor 16 E. I don t know L =4πR 2 σt 4 Suppose you double R while keeping T fixed. What happens to L? 20

21 Using Stefan-Boltzmann Law A.L goes down by a factor 4 B. L stays the same C. L goes up by a factor 4 D.L goes up by a factor 16 E. I don t know L =4πR 2 σt 4 Suppose you double T while keeping R fixed. What happens to L? 21

22 Examples With Stefan-Boltzmann Law L =4πR 2 σt 4 surface area of a sphere Suppose you have a star with some luminosity and you double its radius R while keeping the temperature T fixed. What happens to L? L goes up by a factor of 2x2, or 4 What if you double the temperature T while keeping the radius R fixed? L goes up by a factor of 2x2x2x2, or 16 Note that the other constants are always fixed, so we don t have to worry about them when taking a ratio 22

23 Properties of Thermal Radiation 1. Hotter objects emit more light at all frequencies per unit area. Total luminosity is the area under the curve 23

24 Inverse square law The intensity of light diminishes with the inverse square of the distance from the source 24

25 L1-11 Inverse square law Just a geometrical effect Light from a point source (e.g., a light bulb or a star) gets spread out in all directions. diminishes by the surface are of the sphere is fills apparent brightness b = L 4πd 2 How bright we perceive a star to be depends on both its intrinsic luminosity and its distance from 25 us.

26 Three basic types of spectra Continuous Spectrum Intensity Emission Line Spectrum Absorption Line Spectrum Wavelength Spectra of astrophysical objects are usually combinations of these three basic types. 26

27 Kirchoff s Laws Hot, dense objects emit a continuous spectrum e.g., a light bulb light of all colors & wavelengths follows thermal distribution obeys Wien s & Stefan-Boltzmann Laws. Hot, diffuse gas emits light only at specific wavelengths. emission line spectrum A cool gas obscuring a continuum source will absorb specific wavelengths absorption line spectrum e.g., a neon light e.g., a star 27

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