A source emits light of wavelengths 555 nm and 600 nm. The radiant flux of the 555 nm part is 40 W and of the 600 nm part is 30 W. The relative luminosity at 600 nm is 0-6. Find (a) the total radiant flux, (b) the total luminous flux, (c) the luminous efficiency.

Explanation

To solve the problem step by step, we will follow the instructions provided in the video transcript.

### Step 1: Calculate the Total Radiant Flux
The total radiant flux is the sum of the radiant fluxes of the two wavelengths.

Given:
- Radiant flux at 555 nm = 40 W
- Radiant flux at 600 nm = 30 W

Total Radiant Flux (Φ_r) = Radiant flux at 555 nm + Radiant flux at 600 nm
Φ_r = 40 W + 30 W
Φ_r = 70 W

### Step 2: Calculate the Total Luminous Flux
The luminous flux can be calculated using the formula:
\[ \text{Luminous Flux} = \text{Radiant Flux} \times \text{Relative Luminosity} \]

For 555 nm:
- The luminous flux for 1 W of radiant flux at 555 nm is approximately 685 lumens.
- Therefore, for 40 W:
\[ \text{Luminous Flux at 555 nm} = 40 \, \text{W} \times 685 \, \text{lm/W} = 27400 \, \text{lm} \]

For 600 nm:
- The relative luminosity at 600 nm is given as 0.6.
- Therefore, for 30 W:
\[ \text{Luminous Flux at 600 nm} = 0.6 \times (30 \, \text{W} \times 685 \, \text{lm/W}) \]
\[ = 0.6 \times 20550 \, \text{lm} = 12330 \, \text{lm} \]

Now, we can find the total luminous flux:
\[ \text{Total Luminous Flux} = \text{Luminous Flux at 555 nm} + \text{Luminous Flux at 600 nm} \]
\[ = 27400 \, \text{lm} + 12330 \, \text{lm} = 39730 \, \text{lm} \]

### Step 3: Calculate the Luminous Efficiency
Luminous efficiency is defined as the total luminous flux divided by the total radiant flux.

Using the values calculated:
\[ \text{Luminous Efficiency} = \frac{\text{Total Luminous Flux}}{\text{Total Radiant Flux}} \]
\[ = \frac{39730 \, \text{lm}}{70 \, \text{W}} \]
\[ = 567.6 \, \text{lm/W} \]

This can be approximated to:
\[ \text{Luminous Efficiency} \approx 570 \, \text{lm/W} \]

### Final Answers:
(a) Total Radiant Flux = 70 W
(b) Total Luminous Flux = 39730 lm
(c) Luminous Efficiency = 570 lm/W