CIE A Level Physics (9702) exams from 2022

Revision Notes

25.1.1 Luminosity & Radiant Flux

Defining Luminosity

  • Luminosity L is defined as:

The total power output of radiation emitted by a star

  • It is measured in units of Watts (W)
  • Radiant flux intensity F is defined as:

The observed amount of intensity, or the radiant power transmitted normally though a surface per unit of area, of radiation measured on Earth

  • The best way to picture this is:
    • The luminosity is the total radiation that leaves the star
    • The radiant flux intensity is the amount of radiation measured on Earth
    • By the time the radiation reaches the Earth, it will have spread out a great deal, therefore, it will only be a fraction of the value of the luminosity

Inverse Square Law of Flux

  • Light sources which are further away appear fainter because the light it emits is spread out over a greater area
  • The moment the light leaves the surface of the star, it begins to spread out uniformly through a spherical shell
    • The surface area of a sphere is equal to 4πr2
  • The radius r of this sphere is equal to the distance d between the star and the Earth
  • By the time the radiation reaches the Earth, it has been spread over an area of 4πd2
  • The inverse square law of flux can therefore be calculated using:

Inverse Square Law of Flux equation 1

  • Where:
    • F = radiant flux intensity, or observed intensity on Earth (W m-2)
    • L = luminosity of the source (W)
    • d = distance between the star and the Earth (m)
  • This equation assumes:
    • The power from the star radiates uniformly through space
    • No radiation is absorbed between the star and the Earth
  • This equation tells us:
    • For a given star, the luminosity is constant
    • The radiant flux follows an inverse square law
    • The greater the radiant flux (larger F) measured, the closer the star is to the Earth (smaller d)

Worked example: Inverse square law of flux

Inverse_Square_Law_of_Flux_Worked_Example_-_Calculating_Stellar_Distances_Question, downloadable AS & A Level Physics revision notes

Step 1:            Write down the known quantities

Luminosity, L = 4.8 × 1029 W

Radiant flux intensity, F = 2.6 nW m–2 = 2.6 × 10–9 W m–2

 Step 2:            Write down the inverse square law of flux

Inverse Square Law of Flux Worked Example equation 1

Step 3:            Rearrange for distance d, and calculate

Inverse Square Law of Flux Worked Example equation 2

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