Syllabus Edition

First teaching 2023

First exams 2025

|

Luminosity & Radiant Flux (CIE A Level Physics)

Revision Note

Test yourself
Ashika

Author

Ashika

Last updated

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

Luminosity v Flux, downloadable AS & A Level Physics revision notes

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 4 straight pi r squared
  • 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 4 straight pi d squared
  • The inverse square law of flux can therefore be calculated using:

F space equals space fraction numerator L over denominator 4 straight pi d squared end fraction

  • 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, downloadable AS & A Level Physics revision notes

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

Worked example

A star has a known luminosity of 9.7 × 1027 W. Observations of the star show that the radiant flux intensity of light received on Earth from the star is 114 nW m–2.

Determine the distance of the star from Earth.

Answer:

Step 1: Write down the known quantities

  • Luminosity, L = 9.7 × 1027 W
  • Radiant flux intensity, F = 114 nW m–2 = 114 × 10–9 W m–2

Step 2: Write down the inverse square law of flux

F space equals space fraction numerator L over denominator 4 straight pi d squared end fraction

Step 3: Rearrange for distance d, and calculate

d space equals space square root of fraction numerator L over denominator 4 straight pi F end fraction end root space equals space square root of fraction numerator 9.7 cross times 10 to the power of 27 over denominator 4 straight pi cross times open parentheses 114 cross times 10 to the power of negative 9 end exponent close parentheses end fraction end root

d = 8.2 × 1016 m

You've read 0 of your 10 free revision notes

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Ashika

Author: Ashika

Expertise: Physics Project Lead

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.