Question

A source emits 31.4 W of radiant flux distributed uniformly in all directions. The luminous efficiency is 60 lumen watt−1. What is the luminous intensity of the source?

Answer 1

Dear Student,

◆ Answer -

Luminous intensity = 150 candella

● Explanation -

# Given -

Radiant flux = 31.4 W

Luminous efficiency = 60 lumen/watt

# Solution -

Luminous intensity is given by -

Luminous intensity = luminous flux / solid angle

Luminous intensity = luminous efficiency × radiant flux / solid angle

Luminous intensity = 60 × 31.4 / 4π

Luminous intensity = 150 candella

Hence, the luminous intensity of the source is 150 candella.

Thanks dear. Hope this helps..

Answer 2

The luminous intensity of the source is 150 candela

Explanation:

Step 1:

Given data in the question  :

Radiant flux = 31.4 W

Due to the uniform distribution of the radiant flux in all directions, the solid angle will be 4π

Efficiency  Luminous = $60 lumen / \mathrm{W}$

Step 2:

So,  

We know that

$Total luminous flux = Luminous efficiency \times Radiant flux$

                                = 60  × 31.4  lumen

Step 3:

$Luminous intensity =\frac{\text { Luminous Flux }}{\text { Solid angle }}=\frac{\text { Luminous Flux }}{4 \pi}$

$=\frac{60 \times 31.4}{4 \pi}$

$=\frac{1884}{4 \pi}$

$=\frac{1884}{4 \times 3.14}$

$=\frac{1884}{12.56}$

= 150  candela  

Thus the luminous intensity of the source is 150 candela