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Relative luminosity is defined as the ratio of the luminosity of a particular wavelength to the maximum luminosity. Being a ratio of two identical quantities, it is a dimensionless quantity.

Radiant flux is the total radiant energy emitted per unit time. Its unit is Watt, which is the same as that of power. Thus, radiant flux and power have identical dimensions of $[M L^2 T^{-3}]$.

Luminous flux is measured in lumens, where $1 \text{ lumen} = 1 \text{ candela} \times 1 \text{ steradian}$. Since solid angle (steradian) is a dimensionless quantity, luminous flux has the same dimensions as luminous intensity, which is $[J]$.

Radiant flux has dimensions of $[M L^2 T^{-3}]$, while luminous flux has dimensions of $[J]$. Hence, they do not possess identical dimensions.