Luminosity & Radiant Flux (Cambridge (CIE) A Level Physics)

Defining luminosity

• Luminosity is defined as:

  The total power output of radiation emitted by a star

• It is measured in units of watts (W)

• Radiant flux intensity is defined as:

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

• The difference between luminosity and radiant flux is:

  • luminosity is the total radiation that leaves the star

  • 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

Luminosity and radiant flux of a star

The luminosity is the total power output of the star, whereas the radiant flux is what is measured on Earth

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 

• 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 

• The inverse square law of flux can therefore be calculated using:

• 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)

The inverse square law of flux

Inverse square law; when the light is twice as far away, it has spread over four times the area, hence the intensity is four times smaller