In Radiometry, radiance (L) is defined as flux density per unit area per unit solid angle. If we move further along a ray, away from a point, shouldn't the radiance decrease? I am unable to grasp an intuitive reason for the statement:

Radiance remain constant along rays of light through empty space.

Any explanation in this regard would be highly appreciated.

  • $\begingroup$ A ray is a stream of photons all moving in the same direction. You seem to be confusing that with the case of photons scattered in multiple directions (in which case the overall intensity will diminish with the square of the distance). $\endgroup$ – lemon Apr 22 '15 at 13:52
  • $\begingroup$ Imagine you start right near a star. As you move away from the star the energy falls off as 1/r^2 but the solid angle does too so they cancel out. $\endgroup$ – pentane Apr 22 '15 at 14:35

Imagine you start right next to a star. As you move away from the star, the intensity of the light $I$ (in $W/m^2$) goes down depending on distance $r$ following an inverse-square law:

$$I\ \alpha\ \frac{1}{r^2}$$

but the solid angle $\Omega$ (in $sr$) also decreases in the same proportion:

$$\Omega\ \alpha\ \frac{1}{r^2}$$

Therefore since radiance $L$ (in $W/m^2\cdot sr^{-1}$) is intensity per unit solid angle:

$$L\ \alpha\ \frac{I}{\Omega}$$

the $r^2$ cancels out and radiance does not depend on distance.


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