Mart out the correct options

Options

A. Luminous flux and radian flux have same dimensions
B. Luminous flux and luminous intensity have same dimensions
C. Radiant flux and power have same dimensions
D. Relative luminosity is a dimensionless quantity.

Answer

To solve the question, we need to analyze each option provided in the question regarding luminous flux, radiant flux, luminous intensity, power, and relative luminosity.

### Step-by-Step Solution:

1. **Understanding Luminous Flux and Radiant Flux:**
- Luminous flux (Φ) is the measure of the perceived power of light and is measured in lumens (lm). The unit can also be expressed as candela per steradian (cd/sr).
- Radiant flux (Φe) is the total amount of energy radiated per unit time and is measured in watts (W).
- **Conclusion:** Since the units of luminous flux and radiant flux are different (lumens vs. watts), they do not have the same dimensions.
- **Option A:** Incorrect.

2. **Understanding Luminous Flux and Luminous Intensity:**
- Luminous intensity (I) is the amount of luminous flux emitted per unit solid angle and is measured in candelas (cd).
- The relationship is such that luminous flux (Φ) can be expressed in terms of luminous intensity (I) and the solid angle (Ω) as Φ = I × Ω.
- **Conclusion:** Luminous flux and luminous intensity do not have the same dimensions; they have different units.
- **Option B:** Incorrect.

3. **Understanding Radiant Flux and Power:**
- As previously mentioned, radiant flux is measured in watts (W), which is equivalent to joules per second (J/s).
- Power is also defined as the rate of doing work or energy transfer per unit time, measured in watts (W).
- **Conclusion:** Radiant flux and power have the same dimensions.
- **Option C:** Correct.

4. **Understanding Relative Luminosity:**
- Relative luminosity is defined as the ratio of the luminous flux of a light source to a reference luminous flux. Since it is a ratio of two quantities with the same units, it is dimensionless.
- **Conclusion:** Relative luminosity is indeed a dimensionless quantity.
- **Option D:** Correct.

### Final Answer:
The correct options are:
- **Option C:** Radiant flux and power have the same dimensions.
- **Option D:** Relative luminosity is a dimensionless quantity.