The colour of an object is largely determined by its diffuse reflection…

Concept. In the diffuse (Lambertian) term of the basic illumination model, a surface reflects each colour channel independently of the others. For incident light I = (IR, IG, IB) and diffuse reflection coefficient Kd = (KR, KG, KB), the reflected colour is the channel-wise product (KR·IR, KG·IG, KB·IB). Two consequences follow: a channel whose coefficient is 0 is completely absorbed, and a channel absent from the light cannot be reflected at all — a surface can never show a colour the illumination does not contain.

Application.

1. Read the surface. Kd = (0.8, 0.4, 0) means the surface returns 80% of any incident red, 40% of any incident green, and none of the incident blue.

2. Write each illumination in RGB. Blue light is (0, 0, 1). Magenta light is red plus blue, i.e. (1, 0, 1).

3. Blue light: reflected = (0.8 × 0, 0.4 × 0, 0 × 1) = (0, 0, 0). No red or green arrives to be reflected, and the blue that does arrive meets a zero coefficient, so every channel comes out at zero — the object appears black.

4. Magenta light: reflected = (0.8 × 1, 0.4 × 0, 0 × 1) = (0.8, 0, 0). The blue component of the light is absorbed by the zero blue coefficient and there is no green in the light, so only the red component survives — the object appears red.

5. So the object appears black under blue light and red under magenta light.

Cross-check.

The zero blue coefficient is what extinguishes pure blue illumination entirely; magenta escapes that fate only because it also carries a red component, and red is the channel this surface reflects most strongly. The green coefficient of 0.4 never contributes here, because neither light source contains any green.