5.1 The Behavior of Light

Light is a fascinating phenomenon with both wave and particle properties. Maxwell's electromagnetic model describes light as oscillating electric and magnetic fields, while the particle model introduces photons as fundamental light particles. These dual aspects help explain light's complex behavior.

Understanding light's properties is crucial for astronomy. Wavelength, frequency, and speed are interconnected, influencing how we perceive celestial objects. The relationship between brightness and distance helps astronomers determine the true nature of distant stars and galaxies.

The Nature of Light

Maxwell's electromagnetic model of light

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• Light is an electromagnetic wave consisting of oscillating electric and magnetic fields perpendicular to each other and the direction of propagation
• Maxwell's equations predicted the speed of light based on the properties of electric and magnetic fields
• Hertz experimentally demonstrated the existence of electromagnetic waves (radio waves)
• Light can be polarized, which is consistent with the wave nature of electromagnetic radiation (polarized sunglasses)

Wavelength, frequency and light speed

• Wavelength ($\lambda$) is the distance between two consecutive crests or troughs of a wave (red light has longer wavelength than blue light)
• Frequency ($f$) is the number of wave cycles that pass a fixed point per unit time (blue light has higher frequency than red light)
• Speed of light ($c$) is the speed at which electromagnetic waves propagate through a vacuum, a constant value of approximately 3 x 10^8 m/s
• The speed of light is equal to the product of wavelength and frequency: $c = \lambda f$
  • Higher frequency corresponds to shorter wavelength, and vice versa (gamma rays have high frequency and short wavelength)

Photons and particle model

• Photons are the fundamental particles of light that carry a specific amount of energy determined by their frequency
• Energy of a photon ($E$) is given by: $E = hf$, where $h$ is Planck's constant
• Light exhibits particle-like behavior in certain interactions
  • Photoelectric effect: electrons are ejected from a metal surface when illuminated by light above a certain frequency threshold (solar panels)
  • Compton scattering: photons collide with electrons, transferring energy and momentum (X-ray scattering)
• Wave-particle duality describes light's ability to exhibit both wave-like and particle-like properties

Wave properties of light

• Refraction occurs when light changes speed as it passes from one medium to another, causing it to bend
• Diffraction is the bending of light waves around obstacles or through openings
• Interference is the combination of two or more waves, resulting in a new wave pattern
• The spectrum of light is the range of colors produced when white light is dispersed (dispersion)
• Reflection occurs when light bounces off a surface, changing its direction

Brightness and Distance

Distance and apparent brightness

• The apparent brightness of an object decreases with the square of its distance from the observer (inverse square law)
• Brightness ($B$) is inversely proportional to the square of the distance ($d$): $B \propto \frac{1}{d^2}$
• Luminosity is the intrinsic brightness or total energy output of an object per unit time and remains constant regardless of distance (absolute magnitude)
• Apparent brightness is the observed brightness of an object from Earth and depends on both the object's luminosity and its distance from Earth (apparent magnitude)
• Examples:
  • Sun appears brighter than other stars due to its proximity to Earth (~93 million miles)
  • Distant galaxies (Andromeda) appear fainter than nearby galaxies of similar luminosity (Milky Way)