# 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:

• 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

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

Step 3:            Rearrange for distance d, and calculate

### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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