A light source emits monochromatic light of wavelength 555 nm. The source consumes 100 W of electric power and emits 35 W of radiant flux. Calculate the overall luminous efficiency.

Answer

To calculate the overall luminous efficiency of the light source, we will follow these steps:

### Step 1: Understand the Given Data
- Wavelength of light emitted, \( \lambda = 555 \, \text{nm} \)
- Electric power consumed, \( P_{\text{input}} = 100 \, \text{W} \)
- Radiant flux emitted, \( P_{\text{radiant}} = 35 \, \text{W} \)

### Step 2: Calculate the Luminous Flux
The luminous flux (\( \Phi \)) can be calculated using the radiant flux and the luminous efficacy of the light at the given wavelength. The luminous efficacy for monochromatic light at 555 nm is approximately 685 lumens per watt.

\[ \Phi = P_{\text{radiant}} \times 685 \, \text{lm/W} \]

Substituting the values:

\[ \Phi = 35 \, \text{W} \times 685 \, \text{lm/W} = 23975 \, \text{lm} \]

### Step 3: Calculate Overall Luminous Efficiency
The overall luminous efficiency (\( \eta \)) is defined as the ratio of the total luminous flux to the total power input.

\[ \eta = \frac{\Phi}{P_{\text{input}}} \]

Substituting the values we calculated:

\[ \eta = \frac{23975 \, \text{lm}}{100 \, \text{W}} = 239.75 \, \text{lm/W} \]

### Step 4: Round Off the Result
Rounding off the result gives us:

\[ \eta \approx 240 \, \text{lm/W} \]

### Final Answer
The overall luminous efficiency of the light source is approximately **240 lumens per watt**.

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