Radiant Source Ledgers

Beam Energy Uses Irradiance, Area, and Time

The energy a beam delivers is irradiance times area times exposure time, U = E * A * t, which collapses to power times time for a steady source. It assumes constant irradiance over a fixed area for the whole exposure. Real power drifts, beam area wobbles, and timing and alignment carry measurement uncertainty, so the exact ledger holds only for the stated model inputs.

A finite beam-energy claim cites irradiance, illuminated area, and time. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Beam energy uses irradiance, area, and time

The energy ledger cites a checked irradiance source.

E=IAt=6⋅3⋅4=72 JE=I A t=6\cdot 3\cdot 4=72\ \text{J}
Beam energy ledgerThe finite window makes the energy exact.irradianceSource=boundilluminatedArea=3 m^2timeWindow=4 senergy=72 J

The illuminated area is a new source field

The illuminated surface area is separate from the original beam-area quotient.

As=3 m2,t=4 sA_s=3\ \text{m}^{2},\quad t=4\ \text{s}
Finite energy windowBeam area and surface area cannot be swapped.irradianceSource=boundilluminatedArea=3 m^2timeWindow=4 senergy=72 J