Question

Select the incorrect option:
A. Luminous flux and radiant flux have the same dimensions.
B. Luminous flux and luminous intensity have the same dimensions.
C. Radiant flux and power have the same dimensions.
D. Relative luminosity is a dimensionless quantity.

Answer 1

Hint: Luminous flux: It is the measure of the perceived power of light. This is the power which is received by the human eye. Radiant flux: It is the measure of power radiated through a given area in the form of photons. When radiative flux is incident on the surface, it is often called irradiance. These terms are valid when talking about the light parameters like intensity, etc.

Complete answer:
Luminous flux in short we can say is the energy of light received per unit time per unit solid angle. It is one of the seven basic physical quantities. It has dimension [cd], candela.

Also the radiant power is the energy radiated, absorbed or transmitted per unit time. Since it is also the rate of change of power, so it also has the same dimensions of power i.e. $[ML^2T^{-3}]$.
The major difference between intensity and flux is that flux is related with the power itself, whereas intensity is related to the power per unit solid angle.

Since solid angles don’t have any dimensions, hence luminous intensity is the power of light perceived per unit steradians (S.I. unit of solid angle). Thus it has dimensions: $[ML^2T^{-3}]$.
Thus, dimensions of luminous flux and radiant flux are not the same.

So, the correct answer is “Option A”.

Note:
Dimensions of a physical quantity is the property that gives the indication of many things. However this is not unique for different quantities. There are many physical quantities which have the same dimensions but are entirely different from one another. Torque and energy are examples of these.