Light

Guiding Ideas How fast does light travel (how is this measured)? c = 300,00 km/s (in vacuum), Roemer 1670: Jovian satellite timing over a year How does light behave like a wave? Interference effects How is the light from an ordinary light bulb different from the light emitted by a neon sign? Continuous vs. line radiation How can astronomers measure the surface temperatures of the Sun, stars, planets? Wien’s Law What is a photon? Quantum nature of light, energy prop. to wavelength (duality of wave, particle picture) How can astronomers tell what distant celestial objects are made of? Spectral lines: ‘fingerprints’ of elements What are atoms made of? Structure of atoms (Bohr model) How does the structure of atoms explain what kind of light those atoms can emit or absorb? Bohr model of quantized electron orbits How can we tell if a star is approaching us or receding from us? Doppler effect

Italian Galileo unsuccessfully attempted to measure the speed of light by asking an assistant on a distant hilltop to open a lantern the moment Galileo opened his lantern. Light travels through empty space incredibly fast. For hilltops separated by 10 km, time taken for light is 30 microsec!

Light travels through empty space at a speed of 300,00 km/s, called c In 1676, Danish astronomer Olaus R øe mer discovered that the exact time of eclipses of Jupiter’s moons varied based on how near or far Jupiter was to Earth. This occurs because it takes varying amounts of time for light to travel the varying distance between Earth and Jupiter. 3 ·10 8 km

Light travels through empty space at a speed of 300,00 km/s, called c In 1850, Frenchmen Fizeau and Foucalt showed that light takes a short, but measurable, time to travel by bouncing it off a rotating mirror. The light returns to its source at a slightly different position because the mirror has moved during the time light was traveling a known distance.

White light is composed of all colors which can be separated into a rainbow, or a spectrum, by passing the light through a prism. Visible light has a wavelength ranging from 400 nm (blue) to 700 nm (red). Light is electromagnetic radiation and is characterized by its wavelength

Although Isaac Newton suggested that light was made of tiny particles called P HOTONS 130 years earlier, Thomas Young demonstrated in 1801 that light has wave-like properties. He passed a beam of light through two narrow slits which resulted in a pattern of bright and dark bands on a stream. This is the pattern one would expect if light had wave-like properties.

Imagine water passing through two narrow openings as shown below. As the water moves out, the resulting waves alternatively cancel and reinforce each other, much like what was observed in Young’s Double Slit Experiment . This is the pattern one would expect if light had wave-like properties.

Today, we understand that light has characteristics of both particles and waves. Light behaves according to the same equations that govern electric and magnetic fields that move at 300,000 km/s so light is also called electromagnetic radiation . Electromagnetic radiation consists of oscillating electric and magnetic fields. The distance between two successive wave crests is called the wavelength and is designated by the letter  .

Electromagnetic radiation is produced by stars at a wide variety of wavelengths in addition to visible light. Astronomers sometimes describe EM radiation in terms of frequency,  , instead of wavelength,  . The relationship is: c =  x  Where c is the speed of light, 3 x 10 8 m/s

W IEN’S L AW : The peak wavelength emitted is inversely proportional to the temperature. In other words, the higher the temperature, the shorter the wavelength (bluer) of the light emitted. A dense object emits electromagnetic radiation according to its temperature.

B LACKBODY C URVES : Each of these curves shows the intensity of light emitted at every wavelength for an idealized object (called a “blackbody”) for several different temperatures. These are called blackbody curves . Note that for the objects at the highest temperature, the maximum intensity is at the shorter wavelengths and that the total amount of energy emitted is greatest.

Astronomers most often use the Kelvin or Celsius temperature scales. In the Kelvin scale, the 0 K point is the temperature at which there is essentially no atomic motion is called absolute zero. In the Celsius scale, this point is –273 º C and on the Fahrenheit scale, this point is -460 ºF.

Wien’s law relates wavelength of maximum emission for a particular temperature:  max = 0.0029 T kelvins Stefan-Boltzmann law relates a star’s energy output, called E NERGY F LUX , to its temperature E NERGY F LUX =  T 4 E NERGY F LUX is measured in joules per square meter of a surface per second and  = 5.67 X 10 -8 W m -2 K -4.. Wien’s law and the Stefan-Boltzmann law are useful tools for analyzing glowing objects like stars

Wien’s law relates wavelength of maximum emission for a particular temperature.  max = 0.0029 T kelvins Stefan-Boltzmann law relates a star’s energy output, called E NERGY F LUX , to its temperature. E NERGY F LUX =  T 4 E NERGY F LUX is measured in joules per square meter of a surface per second and  = 5.67 X 10 -8 W m -2 K -4 Energy of a photon ( in terms of wavelength ) E = h c /  where h = 6.625 X 10 -34 J s or where h = 4.135 X 10-15 cV s Energy of a photon ( in terms of frequency ) E = h  where  is the frequency of light These two relationships are called Planck’s law. A few other useful relationships

Each chemical element produces its own unique set of spectral lines.

The brightness of spectral lines depend on conditions in the spectrum’s source.

The brightness of spectral lines depend on conditions in the spectrum’s source. Law 1 A hot opaque body, such as a perfect blackbody, or a hot, dense gas produces a continuous spectrum -- a complete rainbow of colors with without any specific spectral lines. (This is a black body spectrum.)

The brightness of spectral lines depend on conditions in the spectrum’s source. Law 2 A hot, transparent gas produces an emission line spectrum - a series of bright spectral lines against a dark background.

The brightness of spectral lines depend on conditions in the spectrum’s source. Law 3 A cool, transparent gas in front of a source of a continuous spectrum produces an absorption line spectrum - a series of dark spectral lines among the colors of the continuous spectrum.

Features of the Sun’s spectrum created by passing sunlight through a prism.

Emission Line Spectra of A Few Common Elements

Electromagnetic Radiation: Radio Waves (TV,  ~ 1m) Antenna size ~1m

But, where does light actually come from? Light comes from the movement of electrons in atoms.

Rutherford’s Experiment (1915) Showed that Atoms Are Largely Empty Space! Alpha particles from a radioactive source are channeled through a very thin sheet of gold foil. Most pass through showing that atoms are mostly empty space, but a few are rejected showing the tiny nucleus is very massive.

An atom consists of a small, dense nucleus surrounded by electrons ( Note: Nucleus actually much smaller)

An atom consists of a small, dense nucleus surrounded by electrons. The nucleus contains protons and neutrons All atoms with the same number of protons have the same name (called an element ). Atoms with varying numbers of neutrons are called isotopes . Atoms with a varying numbers of electrons are called ions .

Spectral lines are produced when an electron jumps from one energy level to another within an atom.

Bohr’s formula for hydrogen wavelengths 1/  = R x [ 1/N 2 – 1/ n 2 ] N = number of inner orbit n = number of outer orbit R = Rydberg constant (1.097 X 10 7 m -1 )  = wavelength of emitted or absorbed photon

The wavelength of a spectral line is affected by the relative motion between the source and the observer.

Doppler Effect: Caused by Motion

Doppler Shift Red Shift : The distance between the observer and the source is increasing. Blue Shift : The distance between the observer and the source is decreasing.  = wavelength shift,  f = frequency shift  o = wavelength if source is not moving v = velocity of source c = speed of light

Doppler Shift Example A spacecraft on its way to Mars transmits a signal at 100 MHz (1 MHz = 10 6 Hz). It is received on Earth at 99.99 MHz. How fast is the spacecraft moving and in which direction? Since observed frequency is lower, the spacecraft is moving away from Earth.

Chap 5: Key Ideas How fast does light travel (how is this measured)? c = 300,00 km/s (in vacuum), Roemer 1670: Jovian satellite timing over a year How does light behave like a wave? Interference effects How is the light from an ordinary light bulb different from the light emitted by a neon sign? Continuous vs. line radiation How can astronomers measure the surface temperatures of the Sun, stars, planets? Wien’s Law What is a photon? Quantum nature of light, energy prop. to wavelength (duality of wave, particle picture) How can astronomers tell what distant celestial objects are made of? Spectral lines: ‘fingerprints’ of elements What are atoms made of? Structure of atoms (Bohr model) How does the structure of atoms explain what kind of light those atoms can emit or absorb? Bohr model of quantized electron orbits How can we tell if a star is approaching us or receding from us? Doppler effect

PRS Quiz: Nature of light and Spectra List the emission of red, green, and blue light in order of increasing wavelength Blue,green, red Red, green, blue Blue,red, green Green, red, blue Xrays travel at what speed? (c is the speed of light) Faster than c Slower than c At exactly c Depends on the energy of the x-ray The temperature of this room is closest to 290K 25K 273.1K 70K

A dilute hot gas (such as a neon beer sign) emits Emission line spectrum Absorption line spectrum Continuous spectrum Absorption lines superimposed on continuous spectrum Jupiter has a surface temperature of 120K and a blackbody spectrum which peaks at a wavelength of 30 microns. Pluto’s blackbody spectrum peaks at 60 microns. What is its surface temperature? 30K 60K 120K 240K The Doppler effect is a change of wavelength caused by Gravitational fields between emitter and observer Dilute hot gases in the path of the light Magnetic fields near the emitter Relative motion of the source or observer

Light

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