Question

The luminous intensity of $100W$ unidirectional bulb is $100\text{ candela}$. The total luminous flux emitted from bulb will be
$\begin{array}{rl}& \text{A}\text{. }100\pi \text{ lumen}\\ & \text{B}\text{. }200\pi \text{ lumen}\\ & \text{C}\text{. }300\pi \text{ lumen}\\ & \text{D}\text{. }400\pi \text{ lumen}\end{array}$

Answer 1

Hint: Luminous intensity is a quantity for characterising a light source. We will find the relation between luminous flux, luminous intensity and the solid angle to determine the value of luminous flux. For a unidirectional bulb, solid angle will be $4\pi$.

Formula used:
$\text{Luminous flux}=\text{Luminous intensity}\times \text{solid angle}$

Complete step by step answer:
Luminous flux or luminous power in photometry is a measure of the perceived power of light. We can say that luminous power is a measure of the total amount of visible light emitted by a lamp. Luminous intensity can be expressed as the rate of transmission of luminous energy. The SI unit of luminous flux is lumen.
Luminous intensity is a measurement of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle. Luminous intensity is a quantity for characterising a light source. It is described as the luminous flux per unit solid angle. The SI unit of the luminous intensity is the candela, that is, lumen per steradian.
$\text{cd = }{\displaystyle \frac{\text{lm}}{\text{sr}}}$
$\text{Luminous flux}=\text{Luminous intensity}\times \text{solid angle}$
When the luminous angle of a light source is one solid angle and the luminous flux is one lumen, then, its luminous intensity is one candela.
We have,
$\begin{array}{rl}& \text{Luminous intensity}=100W\\ & \text{Solid angle}=4\pi \end{array}$
(For unidirectional bulb, solid angle is considered as $4\pi$)
Therefore,
$\text{Luminous flux}=100\times 4\pi =400\pi$
The total luminous flux emitted from bulb is $400\pi \text{ lumen}$
Hence, the correct option is D.

Note:
Luminous flux is the measure of the total perceived power of light while luminous intensity is a measurement of the perceived power emitted by a light source in a particular direction per unit solid angle. Solid angle is the three dimensional (3d) analogue of an angle.