Common Formulas Dealing with Light

Properties of Light

In these equations, the variables represent the following values:

c = the speed of light, 3.00 x 105 km/s (see Physical Constants)

f = the frequency of light, units of Hz or 1/second

λ = the wavelength of light, units of length

Ε = the energy in a single photon of wavelength λ or frequency f

h = Planck's constant, 6.63 x 10-34 J s (see Physical Constants)

Parallax Formula

d is the distance to the star measured in parsecs

p is the parallax angle of the star measured in arcseconds

Mass and Energy Equivalence

E is the energy, m is the mass, and c = 3.00 x 105 km/s (see Physical Constants)

Blackbody or Thermal Radiation

Wien's Law

The temperature T is given in K. The maximum wavelength will be in units of nanometers.

Stefan-Boltzmann Law and the Relationship between L, R, and T

For an ideal blackbody (which stars are often assumed to be), the relationship between Luminosity, Radius, and Temperature is given by the Stefan-Boltzmann Law.

Luminosity, L = the amount of energy radiated per second

Radius, R = the size of the object

Temperature, T = the blackbody temperature of the object.

Flux = F = the amount of energy radiated per second per area

σ = Stefan-Boltzmann constant = 5.67 x 10-8 W/m2/K4 (see Physical Constants)

Relationship between Luminosity, Flux, and Distance

Luminosity, L = the amount of energy radiated per second

Flux , F = the amount of energy received per second per area at a distance of d

Doppler Shift Equation

Distance and Apparent and Absolute Magnitude

Distance Modulus

m - M = 5 log(d) - 5

m = apparent magnitude

M = absolute magnitude

d = distance in parsecs

if m < M, then d < 10 pc

if m > M, then d > 10 pc

Useful Summary:

http://astro.unl.edu/classaction/outlines/stellarprops/slide5.html

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