Astronomy Notes

Light: Wave or Particle?

• Newton proposed that light is a particle, like little bullets.
• Huygens argued that it is a wave, like sound.
• From 1650-1900 the wave theory was accepted.
• Now it is believed that light is "both" an electromagnetic wave and a particle called a photon.

Waves

• Waves have a wavelength, which is the distance between peaks in the waves.
• Waves have a frequency, which is the number of cycles per second passing a point.
• The frequency times the wavelength equals the speed of the wave: fl = s.
• That means that the higher the frequency, the shorter the wavelength.

The Visible Spectrum of Light

• Newton showed that white light is made up of all the colors of the rainbow.
• The colors of the spectrum are red, orange, yellow, green, blue and violet
• The wavelength of light goes from 400 (violet) to 700 (red) nm ( 1 nm = nanometer = 10^-9 meter).

The Full Spectrum of Light

• Visible light is only a tiny portion of the entire electromagnetic spectrum.
• Gamma Rays are super high energy, very short wavelength, being about 0.01 nm.
• X-ray are very high energy so they penetrate flesh but not bones, being about 0.1 to 1.0 nm.
• Ultraviolet waves are too short to see, being in the 10-100 nm range.
• Visible light is 400-700 nm, going from violet to red.
• Infrared waves are too long to see, being in the 1 - 100 µ range (i.e. 1,000 nm to 0.1 mm).
• Microwaves are in the .1 mm to 1 mm range.
• Radio waves extend from 1 cm to many km in wavelength.

The relation of wavelength and frequency for light

• The speed of light is constant, and is called simply "c". It equals 3.0 x 10⁸m/sec.
• So frequency x wavelength = speed, or fl = c.
• Example: What is the wavelength of FM 100 waves? (100 means 100 MHz, or 100 million cycles per sec.)
  • l = c/f = 3 x 10⁸m/sec / 100 x 10⁶/sec
  • l = 3 m. So the wavelength of music on FM radio is about 3 meters. (10 feet).
  • AM radio (at 1000 KHz) is about 300 meters.

Wave Properties of light

• Refraction: light slows down in a transparent medium, causing it to bend.
• Dispersion: Refraction depends on wavelength, causing blue to bend more than red, giving rainbows
• Diffraction: Light bends around corners.
• Doppler Effect: If a light source is moving away from us, it's spectrum is shifted towards the red.

Particle Properties of light

• Light comes in discrete units, like little bullets, called photons
• The photoelectric effect:
  • A tiny blue light can knock some electrons off a metal plate.
  • A bright red beacon cannot eject any electrons from the same plate.
  • Hence, light cannot be a wave, or the huge red light would eject at least a few electrons.
  • It must be that blue light is like high power bullets, and red light like BB's.
  • The energy of light is proportional to its frequency: E = hf, where h is a constant.

Temperature

• Temperature is a measure of the average speed of a body's molecular motion.
• Astronomers use absolute temperature measured in degrees Kelvin, or simply Kelvins.
• One kelvin is the same as 1° C.
• Absolute zero = 0 K = -273° C is where essentially all motion stops.

Thermal Radiation

• All objects radiate (give off light) according to their temperature.
• Wien's Law: The hotter an object, the bluer the radiation it emits.
• (The hotter an object the more light it emits at all wavelengths, but the peak shifts towards blue.)
• Wavelength varies inversely with temperature: 10 times the temperature = 1/10 the wavelength.

Emission Lines

• A hot gas does not emit a smooth spectrum as do hot solid or liquid bodies.
• Instead, the light it emits is restricted to a few very precise wavelengths called emission lines.
• The theory is that electrons are dropping down fixed energy levels in the atomic electron shells.
• Electrons in the lowest energy level are in the "ground state." Others are in "excited states."
• The most important visible line is the red line called H alpha in hydrogen gas.

Absorption Lines

• When light passes through a cool gas, it absorbs out the same lines that it would emit if hot.
• Thus the light spectrum has black lines in it which identify the element and its temperature.

Molecular lines

• Molecules give off groups of narrowly spaced lines called bands.
• They are much lower energy than atoms and tend to be in the infrared wavelengths.
• There are both emission and absorption lines for molecules, as for atoms.
• Water vapor absorbs much infrared light, so observatories are on mountains to get above it.

Telescopes come in two varieties

• Refractors use a lens for the principal objective.
• Reflectors use a mirror for the objective.

• Magnification is the increase in apparent angular diameter of an object.
• Resolution measures the smallest angular separation between two objects that can seen.
• Light-gathering power measures how much more light it sees compared to the unaided eye.

What to look for in a telescope

• Magnification comes from a long focal length, combined with eyepieces of short focal length.
• Resolution comes from a large diameter objective (and high quality optics).
• Light-gathering power comes from a large diameter objective.
• Therefore, the most important feature of a telescope is the size of the objective.

All big telescopes are reflectors

• Lenses have chromatic aberration, causing red and blue fringes on images. Mirrors don't do that.
• Mirrors can be supported all across the back so the reflecting shape does not sag.
• Reflectors are shorter, so they don't suffer from long flexing tubes.
• Mirrors are cheaper than lenses because the light does not have pass through the glass.

Why a pair of good 10 x 50 binoculars for $50 are better than a 100x 60 mm telescope for $100.

• They have just as much light gathering power. 10 x 50 means 10 power, 50 mm diameter.
• Most objects in the sky are dim, not small, so it is only light gathering power that is needed.
• The Andromeda galaxy covers about 3° (6 moon diameters) of sky. It is just too dim to see more than the tiny center with the unaided eye.
• The Andromeda galaxy looks about the same in either binoculars or a small telescope.
  • It is 10 times larger in a telescope, but 10 times dimmer because the light is spread out.
  • So you can only see about a tenth as much, ten times bigger, so it looks the same.
• You can take binoculars to football games and operas, or go birdwatching.

Astronomers usually replace visual observations with instruments.

• Photographic images can be digitized and made into false color images.
• Photometers measure the brightness of objects.
• Spectrophotometers measure the brightness in different colors.

Space Telescopes have great advantages

• Eliminates all distortion from the air.
• Allows ultraviolet, x-ray and gamma-ray astronomy.
• The background is a million times darker for infra-red astronomy because the earth radiates.

Radio Telescopes

• The long wavelengths require huge antennas, so they are ground based.
• The long wavelengths yield very poor resolution.
• Interferometry used many widely separated telescope to improve resolution by blending signals.