A source emits 31.4 W of radiant flux distributed uniformly in all directions. The luminous efficiency is 60 lumen watt. What is the luminous intensity of the source ?

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Identify the given values
- **Radiant flux (Φ)** = 31.4 W
- **Luminous efficiency (η)** = 60 lumen/W

### Step 2: Calculate the luminous flux (Φv)
Luminous flux can be calculated using the formula:
\[ \Phi_v = \eta \times \Phi \]
Substituting the known values:
\[ \Phi_v = 60 \, \text{lumen/W} \times 31.4 \, \text{W} = 1884 \, \text{lumen} \]

### Step 3: Determine the solid angle (Ω)
Since the radiant flux is distributed uniformly in all directions, the solid angle for a point source is:
\[ \Omega = 4\pi \, \text{steradians} \]

### Step 4: Calculate the luminous intensity (I)
Luminous intensity can be calculated using the formula:
\[ I = \frac{\Phi_v}{\Omega} \]
Substituting the values we have:
\[ I = \frac{1884 \, \text{lumen}}{4\pi} \]
Using the approximation \( \pi \approx 3.14 \):
\[ I = \frac{1884}{4 \times 3.14} = \frac{1884}{12.56} \approx 150 \, \text{candela} \]

### Final Answer
The luminous intensity of the source is approximately **150 candela**.

---