Inverse Square Law of Radiation

• What is the Inverse Square Law of Radiation?

  It describes how brightness decreases with distance

  
• What is luminosity defined as?

  The total power output of radiation emitted by a star
• In what units is luminosity measured?

  Watts (W)
• How is brightness defined?

  The intensity of radiation received on Earth from a star

  
• What does brightness measure in terms of light?

  Power per unit area, or light intensity
• In what units is brightness measured?

  Watts per metre squared (W m^-2)
• What are the two main factors that affect the brightness of a star?

  Its luminosity and distance from Earth

  
• How does distance affect the brightness of a star?

  More distant stars are usually fainter
• What is the difference between brightness and luminosity?

  Brightness is measured on Earth, luminosity is total output
• Why is knowing luminosity and brightness useful?

  It helps determine the distance of the star from Earth

  
• What happens to radiation from a distant star as it reaches Earth?

  It spreads out over a very large area
• What does the inverse square law of radiation state about light sources?

  Farther sources appear fainter due to area spread

  
• What is the surface area formula of a sphere?

  4πr²
• What does the radius r of the sphere represent in this context?

  The distance d between the star and the Earth
• How does light intensity change when the distance is doubled?

  It becomes four times smaller
• What is the formula for the inverse square law of radiation?


  I = L / (4πd²)

  
• What does the equation I = L / (4πd²) assume?

  The source can be treated as a point
• What does the equation I = L / (4πd²) tell us about luminosity?

  For a given star, luminosity is constant
• What can be inferred about stars with the same luminosity?

  The star with greater brightness is closer
• If a star has a luminosity of $9.7 \times 10^{27} \text{ W}$, what is the first step to find its distance?


  Write down the known quantities
• How do you rearrange the inverse square law for distance d?

  d = L / (4πI)
• What is the distance of the star from Earth if luminosity is $9.7 \times 10^{27} \text{ W}$ and intensity is $114 \times 10^{-9} \text{ W m}^{-2}$?


  d = $8.2 \times 10^{16} \text{ m}$
• What is an important tip when calculating distance using the inverse square law?

  Square the distance or take the square root