Power received per unit area, perpendicular to the radiation, in W m⁻².

Where does the 4πd² come from?

It is the surface area of a sphere of radius d, over which the star's power is spread.

State two assumptions in using I = L/4πd².

The star radiates equally in all directions; no light is absorbed or scattered between the star and the observer.

Two stars give the same intensity at the Earth, and one has four times the luminosity of the other. Compare their distances.

The more luminous star is twice as far away.

Why is luminosity not the same as how bright a star looks?

Apparent brightness (intensity) also depends on the distance from the star.

Luminosity and intensity of starsEdexcel A-Level Physics: Flashcards

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Define the luminosity of a star.

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Define the luminosity of a star.: The total power it radiates in all directions across all wavelengths, in watts.
Define intensity.: Power received per unit area, perpendicular to the radiation, in W m⁻².
State the equation linking intensity, luminosity and distance.: $I = \dfrac{L}{4\pi d^2}$
Where does the 4πd² come from?: It is the surface area of a sphere of radius d, over which the star's power is spread.
What happens to the intensity if the distance from a star doubles?: It falls to one quarter.
What happens to the intensity if the distance from a star triples?: It falls to one ninth.
State two assumptions in using I = L/4πd².: The star radiates equally in all directions; no light is absorbed or scattered between the star and the observer.
Rearrange I = L/4πd² to find the distance.: $d = \sqrt{\dfrac{L}{4\pi I}}$
Rearrange I = L/4πd² to find the luminosity.: $L = 4\pi d^2 I$
What is the luminosity of the Sun?: $3.85 \times 10^{26}$ W
Two stars give the same intensity at the Earth, and one has four times the luminosity of the other. Compare their distances.: The more luminous star is twice as far away.
Why is luminosity not the same as how bright a star looks?: Apparent brightness (intensity) also depends on the distance from the star.

Exam questions on Luminosity and intensity of stars

An astronomer measures the intensity of the light received from distant stars using a telescope fitted with a sensitive detector.
Explain why the intensity of the light received from a star decreases as the distance from the star increases.2 marks
The Sun has a luminosity of 3.85 × 10²⁶ W. The mean distance from the Sun to the Earth is 1.5 × 10¹¹ m. Assume that the Sun radiates equally in all directions and that no radiation is absorbed on its way to the planets.
The planet Mars is 2.3 × 10¹¹ m from the Sun. Calculate the intensity of sunlight at Mars.2 marks
Astronomers measure the intensity of light from a bright star, S, as 1.2 × 10⁻⁷ W m⁻² at the Earth. Star S is 8.1 × 10¹⁶ m from the Earth.
Calculate the luminosity of star S.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).