Question

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.

Answer 1

(a) The total radiant flux is 70 W.

(b) The total luminous flux is 39730 lumen.

(c) The luminous efficiency is 567.6 lumen/W.

Given:

The radiant flux of the 555 nm part is 40 W

The radiant flux of the 600 nm part is 30 W

The relative luminosity at 600 nm is 0.6

Solution:

(a) Total radiant flux is the sum of radiant flux of the 555 nm and radiant flux of the 600 nm.

Total radiant flux = 40 + 30

Therefore, total radiant flux = 70 W

(b) Total luminous flux is the sum of luminous flux of the 555 nm and luminous flux of the 600 nm.

Luminous flux = Radiant power × luminous efficacy × 683 lumens/watt

Total luminous flux $= (1 \times 40 \times 685)+(0.6 \times 30 \times 685)$

Therefore, total luminous flux = 39730 lumen

(c) The luminous efficiency is given by the formula:

$\text { Luminous efficiency} =\frac{\text { Total luminous flux }}{\text { Total radiant flux }}$

$\text{Luminous efficiency}=\frac{39730}{70}$

$\therefore \text{Luminous efficiency} =567.6 \text { lumen} / \mathrm{W}$

Answer 2

(a) The total radiant flux is 70 W

(b) The total luminous flux is 39730 lumen

(c) The luminous efficiency is 568 lumen/W.

Explanation:

Given data in the question  

The radiant 555 Nm wavelength light flux is 40 W.

The luminous flux of wavelength light 600 nm is 30 W.

At 600 nm the relative luminosity is 0.6.

(a) The total radiant flux:

Maximum radiant flux = 555 nm of light part + 600 nm of light part radiant flux

                                      = 40 W + 30 W

                                      = 70 W

(b) The total luminous flux:

Net  luminous flux = 555 nm of light part + 600 nm of light part luminous flux

                                    = 1 × 40 × 685 + 0.6 × 30 × 685

                                    = 39730 lumen

(c)  The luminous efficiency:

$Luminous efficiency =\frac{\text { Total luminous flux }}{\text { Total radiant flux }}$

                                  $= \frac{39730}{70}$

                                  = 567.6 lumen/W

Therefore the luminous efficiency is 568 lumen/W.