Use an ideal three-component light model: R means red, G green and B blue. A beam carries 2 J in R, 3 J in G and 5 J in B during one exposure. Filter 1 transmits only GB; filter 2 transmits only B; an opaque surface reflects only RGB. 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: B. Reflected: B, giving blue. Reflected energy 5 J, or 50% of the original 10 J. Treat each colour component separately. The initial total energy is 2 + 3 + 5 = 10 J; an ideal filter removes components rather than converting one colour into another. A component must be allowed by both GB and B to reach the object. Their common transmitted set is B, carrying 5 J in total. The surface can reflect only components it both receives and is specified to reflect. Intersect the arriving set with RGB: the reflected set is B. This gives the model colour blue. The surviving component energies sum to 5 J, so the reflected fraction is 5/10 and the percentage is 50%. The remaining 5 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.

A white object behind blue filters

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