Final answer:
Lux is the unit of illumination corresponding to the number of lumens per square meter and shares its name with a brand of soap and detergent.
Step-by-step explanation:
The unit of illumination that shares its name with an old brand of soap and detergent is lux (a). Lux is the unit of illuminance, which is the measure of luminous flux per unit area. It is represented as the number of lumens per square meter. The other options, lumen (b), candela (c), and watt (d), represent different aspects of lighting. Lumen measures luminous flux or the total amount of visible light emitted by a source. Candela is the unit of luminous intensity, which refers to the brightness of light emitted in a particular direction, equivalent to the light from a single candle. Lastly, watt is a unit of power that indicates the rate of energy consumption but does not directly measure light output.