21.2 Radiant Flux Intensity

21.2 Radiant Flux Intensity

Radiant flux intensity is the amount of electromagnetic energy per unit area per unit time emitted from a star that reaches the Earth's surface. It is a small fraction of the total value of luminosity. In other words, radiant flux intensity is the luminosity per unit area measured on the surface of Earth. Radiant flux intensity from a star at a distance $d$ is expressed as:

where $L$ is the luminosity and $4\pi r^{2}$ is the surface area of star. As the luminosity of a star remains constant, therefore, radiant flux intensity follows inverse square law with distance as demonstrated in Fig. 21.1. According to this law, when the distance from centre of a star is doubled (from $r$ to $2r$), intensity of the radiant flux reduces to one-fourth of its original value. Similarly, increasing the distance to three times its initial length ($3r$), decreases the flux by a factor of nine, and this pattern continues accordingly.

Tidbit!

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If Earth were twice as far from the Sun, the sunlight reaching it would be only one-fourth as intense. Such low energy might have made the evolution of life impossible.

(Fig. 21.1: Schematic illustration of the inverse-square law for radiant flux intensity)

Brain Teaser

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Two stars appear equally bright in the night sky. However, one is $10$ times farther away than the other. Which star is more luminous, and by how much?

Example 21.2

The luminosity of a star is $4.50 \times 10^{26}\,\mathrm{W}$. It is located at a distance of $1.40 \times 10^{17}\,\mathrm{m}$ from a planet. Calculate the radiant flux intensity of the star at the surface of that planet.

Solution

Luminosity of the star $L = 4.50 \times 10^{26}\,\mathrm{W}$ Distance between Earth and the star $r = 1.40 \times 10^{17}\,\mathrm{m}$ Radiant flux intensity $F = ?$ Using the formula; $F = L / 4\pi r^{2}$ $= 4.50 \times 10^{26}\,\mathrm{W} / (4 \times 3.14(1.40 \times 10^{17}\,\mathrm{m})^{2})$ $F = 1.83 \times 10^{-9}\,\mathrm{W\,m^{-2}}$

Do you know?

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The idea of standard candles dates back to the 1910s, when Henrietta Swan Leavitt discovered that Cepheid variable stars pulse in a predictable way. Her work laid the foundation for measuring cosmic distances and the scale of the universe. Without standard candles, we would not even know how big the universe is.