1. The Continuous Spectrum of Light
Stellar Parallax
The Magnitude Scale
The Wave Nature of Light
Blackbody Radiation
The Quantization of Energy
The Color Index

2. Stellar Parallax
Trigonometric Parallax: Determine distance from “triangulation”
Parallax Angle: One-half the maximum angular displacement due to the motion of Earth about the Sun (excluding proper motion)
With p measured in radians

3. PARSEC/Light Year 1 radian = 57.2957795 = 206264.806”
Using p” in units of arcsec we have:
Astronomical Unit of distance:
PARSEC = Parallax Second = pc
1pc = x 105 AU
The distance to a star whose parallax angle p=1” is 1pc. 1pc is the distance at which 1 AU subtends an angle of 1”
Light year : 1 ly = x 1015 m
1 pc = ly
Nearest star proxima centauri has a parallax angle of 0.77”
Not measured until 1838 by Friedrich Wilhelm Bessel
Hipparcos satellite measurement accuracy approaches 0.001” for over 118,000 stars. This corresponds to a a distance of only 1000 pc (only 1/8 of way to centerof our galaxy)
The planned Space Interferometry Mission will be able to determine parallax angles as small as 4 microarcsec = ”) leading to distance measurements of objects up to 250 kpc.

4. Parallax determination of distance to Venus

5. The Magnitude Scale
Apparent Magnitude: How bright an object appears. Hipparchus invented a scale to describe how bright a star appeared in the sky. He gave the dimmest stars a magnitude 6 and the brightest magnitude 1. Wonderful … smaller number means “bigger” brightness!!!
The human eye responds to brightness logarithmically. Turns out that a difference of 5 magnitudes on Hipparchus’ scale corresponds to a factor of 100 in brightness. Therefore a 1 magnitude difference corresponds to a brightness ratio of 1001/5=2.512.
Nowadays can measure apparent brightness to an accuracy of 0.01 magnitudes and differences to magnitudes
Hipparchus’ scale extended to m= for the Sun to approximately m=30 for the faintest object detectable

6. Flux, Luminosity and the Inverse Square Law
Radiant flux F is the total amount of light energy of all wavelengths that crosses a unit area oriented perpendicular to the direction of the light’s travel per unit time…Joules/s=Watt
Depends on the Intrinsic Luminosity (energy emitted per second) as well as the distance to the object
Inverse Square Law:

7. Absolute Magnitude and Distance Modulus
Absolute Magnitude, M: Defined to be the apparent magnitude a star would have if it were located at a distance of 10pc.
Ratio of fluxes for objects of apparent magnitudes m1 and m2 .
Taking logarithm of each side
Distance Modulus: The connection between a star’s apparent magnitude, m , and absolute magnitude, M, and its distance, d, may be found by using the inverse square law and the equation that relates two magnitudes.
Where F10 is the flux that would be received if the star were at a distance of 10 pc and d is the star’s distance measured in pc. Solving for d gives:
The quantity m-M is a measure of the distance to a star and is called the star’s distance modulus

8. The Continuous Spectrum of Light
The Nature of Light
Blackbody Radiation
The Color Index

9. (will come back to this topic..soon)
Speed of Light
Ole Roemer( ) measured the speed of light by observing that the observed time of the eclipses of Jupiter’s moons depended on how distant the Earth was from Jupiter. He estimated that the speed of light was 2.2 x 108 m/s from these observations. The defined value is now c= x 108 m/s (in vacuum). The meter is derived from this value.
Measurement of speed of light is the same for all inertial reference frames!!!
Special Relativity
(will come back to this topic..soon)
Takes an additional 16.5 minutes for light to travel 2AU

10. The Nature of Light
Newton believed that like was “corpuscular”, particle-like in nature…due to sharpness of shadows.
Christian Huygens ( ) believed that light was wave-like, with a distance between succesive peaks (troughs) of wavelength and that the number of waves per second that pass a point in space is the frequency of the wave. The speed of light is then given by :
Particle and wave models could explain reflection and refraction of light…wave nature of light demonstrated by Thomas Young’s double slit experiment…

11. The Wave Nature of Light
Light impinging on double slit
Exhibits Inerference pattern
Interference condition
(n=0,1,2,…for bright fringes)
(n=1,2,…for dark fringes)
INTERFERENCE
WAVE

12. And God said…let there be light
What is Light?
And God said…let there be light
Maxwell’s Equations in
Free space
Electromagnetic
Wave equation
and there was light….

13. Wavelike Nature of light
Light is an electromagnetic phenomenon
Heinrich Hertz’s Apparatus for the production and detection of radio waves
Deutsches Museum Munich
Changing electric field
Changing Magnetic Field
Propagates through free space
Nothing is waving!!!!
EM waves created by accelerating charges

14. Accelerating Charge causes Electromagnetic Waves
Electric Field emanates from electric charges
What happens to field when charge is accelerated?
“Kink” in electro-magnetic field propagates with finite velocity

15. Electromagnetic Waves
Electromagnetic Wave speed
Light is indeed an
Electromagnetic Wave
Waves are Transverse

16. Electromagnetic Spectrum
Region
Wavelength
Gamma Ray
nm
X-Ray
1 nm<10 nm
Ultraviolet
10 nm<400 nm
Visible
400 nm<700 nm
Infrared
700 nm<1 mm
Microwave
1mm<10 cm
Radio
10 cm<

17. Radiation Pressure and the Poynting Vector
The rate at which energy is carried by a light wave is described by the Poynting vector.
Instantaneous flow of energy per unit area per unit time (W/m2) for all wavelengths.
Points in the direction of the electromagnetic wave’s propagation.
Radiant Flux: Time average (over one period) of the Poynting vector
Because an electromagnetic wave carries momentum it can exert a force on a surface hit by light…
Radiation Pressure
Radiation Pressure is significant in
extremely luminous objects such as:
early main-sequence stars
red supergiants
Accreting compact stars
Interstellar medium dust particles
absorption)
reflection)

18. Photon Flux Densities Light Source Photon Flux Density
Photons/(sec m2)
Laserbeam (10 mW,He-Ne 20um)
Laserbeam (1 mW,He-Ne )
Bright Sunlight
Indoor Light Level
Twilight
Moonlight
Starlight

19. Particle-like nature of light Photons
Photon = “Particle of Electromagnetic “stuff””
Blackbody Radiation
Failure of Classical Theory
Radiation is “quantized”
Photo-electric effect (applet)
Light is absorbed and emitted in tiny discrete bursts

20. Color/Temperature Relation
Betelguese( K)
What does the color of a celestial object tell us? 
Rigel ( ,000K)