A sample sits in the optical path as another transfer stage, reducing the signal by its own fraction rather than through a Beer-Lambert absorbance law. The optical stage passes 1/2 of the source 24, then the sample transfer is 1/3, giving output 24 times 1/2 times 1/3 = 4 exactly for the stated toy transfer ledger; real samples scatter, bleach, saturate, vary spatially, and carry measurement uncertainty.

A sample stage can reduce a deterministic optical signal. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The optics set the incoming signal

The optical stage passes 1/2 of the source.

Safter optics=24⋅12S_{\text{after optics}}=24\cdot\frac{1}{2}
Optical transferExact stage transfers set the output signal.sourcestagestage24124

The sample adds one more transfer

The sample transfer is 1/3, so the output is 4. This is not Beer Lambert absorbance.

Ssample=24⋅12⋅13=4S_{\text{sample}}=24\cdot\frac{1}{2}\cdot\frac{1}{3}=4
Optical transferExact stage transfers set the output signal.sourcestagestage24124