Use an ideal three-component light model: R means red, G green and B blue. A beam carries 3 J in R, 4 J in G and 3 J in B during one exposure. Filter 1 transmits only RG; filter 2 transmits only RGB; an opaque surface reflects only B. Listed components are transmitted or reflected completely; all other energy is absorbed, with no re-emission. Trace the surviving components, state the observed surface colour, and calculate reflected energy and the percentage of incident energy reflected. Equal surviving components mix as RG = yellow, RB = magenta and GB = cyan; unequal energies can change the exact shade.

Question

Accepted Answer

After both filters: R + G. Reflected: none, giving black (no reflected component). Reflected energy 0 J, or 0% of the original 10 J. Treat each colour component separately. The initial total energy is 3 + 4 + 3 = 10 J; an ideal filter removes components rather than converting one colour into another. A component must be allowed by both RG and RGB to reach the object. Their common transmitted set is R + G, carrying 7 J in total. The surface can reflect only components it both receives and is specified to reflect. Intersect the arriving set with B: the reflected set is empty. This gives the model colour black (no reflected component). The surviving component energies sum to 0 J, so the reflected fraction is 0/10 and the percentage is 0%. The remaining 10 J is absorbed by the filters or the opaque surface under the stated model. Real filters have partial transmission and real perceived shades depend on component balance; the ideal component answer does not claim a precise real-world colour match.

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